Three consecutive integers have a sum of 51. The sum of these three integers is equal to 51.

Three consecutive integers have a sum of 51. The sum of these three integers is equal to 51.

Three consecutive integers have a sum of 51. Sum of three consecutive integers is 51 we have to find the three unknown integers that are consecuti Sep 11, 2017 · An additional example of consecutive odd integers would be -1, 1, and 3, whose sum would be 3. So, the three consecutive odd integers whose sum is 51 are and . Therefore, the correct option is D. Jan 24, 2018 · There are three consecutive integers. May 14, 2017 · First, divide 51 by 3, since our consecutive integers will be in that number range. This is found by defining the integers as 47, 49, and 51. Ans: Hint: To find the number, we consider an odd number x, write its next consecutive numbers, add all of them and equate them to 51. The sum of the first two is 51 more than the third. The odd counting numbers, for example, are consecutive odd integers. Simplify the equation: - First, combine like terms: - Combine the terms: 4. Show Video Mar 24, 2025 · To find the greatest of three consecutive integers whose sum is 51, let's break it down step by step: Define the integers: We'll say the three consecutive integers are x, x +1, and x + 2. Find the value of the middle of the three. Another example is 7,8,9. Sum of 3 consecutive integers This calculator has 1 input. 51 / 3 = 17. Let's denote the three consecutive integers as n, n + 1, and n + 2. The key is to have a good grasp of what odd integers are and how consecutive odd integers can be represented. Jan 21, 2024 · Therefore, the three consecutive integers that add up to 51 are 16, 17, and 18. By isolating x, we determined the values of the three numbers. Apr 25, 2022 · To find how many sets of three consecutive integers have a sum between 51 and 60, we can start by representing three consecutive integers mathematically. Three consecutive odd integers have a sum of 21. Find the integers. Sum of Consecutive Integers Word Problems When solving word problems involving consecutive integers, it’s important to remember that we are looking for integers that are one unit apart. We represent any two consecutive integers as n, n + 1 where n ϵ Z. Nov 8, 2024 · The three consecutive odd numbers that add up to 51 are 15, 17, and 19. The sum of these three integers is: (x - 1) + x + (x + 1) = 51 Simplifying the equation: 3x = 51 Solving for : x = \frac {51} {3} = 17 So, the middle integer is . Solving for x yields x=34. After solving, the integers are found to be 16, 17, and 18, with 18 being the largest. The sum of these three integers is equal to 51. Find three consecutive odd integers that have a sum of -51" Math Algebra Algebra questions and answers Three consecutive integers have a sum of 51. ☛ Related Questions: The sum of three consecutive multiples of 8 is 888. This highlights the pattern and process of finding consecutive odd integers, even when the sum involves negative numbers. Oct 29, 2019 · To find three consecutive integers that sum up to 51, let's represent the smallest of these integers as x. The next consecutive odd integers would be x+2 and x+4 (since odd numbers are two units apart). The largest one is 18 and this is the answer. Oct 4, 2024 · Three consecutive integers have a sum of 51. 6, 7, and 8 add up to a number that ends in the ones place. So, we'll set up the equation: x +(x + 1) + (x + 2 Jun 24, 2019 · An example of consecutive numbers would be 1, 2, and 3, which also have a defined sum that can be analyzed similarly. For example, any four integers in a row must have a multiple of 4; any 19 integers will have one multiple of 19 and so on. We found these by defining the first number as x and solving the equation derived from their sum. This is confirmed by checking that the sum of the first two integers equals 51 more than the third integer. Find the numbers. The next two consecutive integers will then be expressed as x + 1 and x + 2. Oct 3, 2024 · To find three consecutive integers whose sum is 51, we will set up an equation based on the properties of consecutive integers. Oct 5, 2024 · The first of three consecutive integers whose sum is between 51 and 72 inclusive is at least 16. Aug 25, 2022 · To find three consecutive odd integers that sum to -51, we can start by defining the first odd integer as x. We'll call them x, x +1, and x + 2. Nov 2, 2022 · What are three consecutive even integers whose sum is 396? 3 consecutive even integers whose sum is 396 are 130, 132 and 134. For example, 1, 2, and 3 are consecutive integers. By following the steps, we find that the three consecutive integers are 15, 16, and 17. Oct 23, 2020 · This answer is FREE! See the answer to your question: Find three consecutive integers that have a sum of 51. Find the multiples. Hence, the middle one is 17. Apr 28, 2022 · Divide the sum of the three consecutive odd integers by 3: 51 / 3 = 17. x + x + 2 + x + 4 = -51 You finish. Thus, -16 is the largest integer. Setting up an Equation: The sum of these integers is given as 51, so we can write the equation: n + (n+1) + (n+2) = 51 Solving the Equation: We will solve the equation for 'n' to find the first integer. However, the question asks for the largest number, which is x+4 or 38. Aug 8, 2025 · Thus, we can say that consecutive integers are the number that follows a regular pattern of writing and there is a fixed difference between any two consecutive integers, i. Mar 18, 2015 · for a more relevant answer The third odd integer among three consecutive odd integers that sum to 147 is 51. Define the Consecutive Integers: Jul 23, 2025 · Sum of Consecutive Numbers We have studied earlier that a consecutive number always differs by the same value i. This method can be applied to any similar problem where you need to find consecutive integers based on their sum! The word “consecutive” means one right after the other. Now, the sum of these integers is equal to 51. To find the three consecutive integers, first divide the sum (51) by 3 to find the middle integer: 51 ÷ 3 = 17. asked • 02/10/18 Integers for the sum of 51 Three consecutive integers have a sum of 51 Follow • 3 Add comment Oct 12, 2024 · The solution for the greatest of three consecutive integers that sum to -51 is -16. e. Write an equation to model this situation, and solve the equation to find the value of the three integers. Consecutive Odd Integers They are odd integers that follow each other in a sequence, so the difference between them is 2. We want to find 3 consecutive integers that add up to 54, so we'll need to add n, n + 1, and n +2 together, set their sum equal to 54, and solve for n to find them. The middle integer of the three consecutive integers that sum to -51 is -17. Detailed step by step solution for the sum of three consecutive integers is 51. Jun 22, 2021 · Three consecutive integers have a sum of − 51 ( The least of the three integers ) ( -17 ) A)The quantity in Column A is greater. The sum is 3x+6, which is equal to 108. Oct 24, 2023 · To find the three consecutive odd integers that sum to 51, we can set up an equation and solve for the unknown values. In general, a sequence of consecutive integers is a sequence of numbers where each term is one more than the Jun 8, 2022 · Therefore, the consecutive odd integers will be 2n+3 and 2n+5 If the sum of the consecutive odd integers is 51 then: To find the values of the integers, substitute the found value of n into the expressions: Therefore, the three consecutive odd integers that sum to 51 are 15, 17 and 19. Aug 3, 2023 · Consecutive integers can be of even odd, even, positive, or negative numbers. To make this task easier and more efficient Jul 20, 2016 · The second odd number in the sequence of three consecutive odd numbers that sum to 51 is 17. Consecutive odd integer problems involve finding a sequence of odd numbers that follow each other in order (like 3, 5, 7) and satisfy a given condition, often involving their sum or product. What are the three numbers? Set up an equation where our numbers are n, n + 1, and n + 2 n + (n + 1) + (n + 2) = Group variables and constants together: (n + n + n) + 1 + 2 = 3n + 3 = Subtract 3 from each side: 3n + 3 - 3 = - 3 Cancel the 3 on the left side and we get: 3n = -3 Divide each side of the equation by 3 to isolate n: Cancel the 3 on the Aug 10, 2017 · To find three consecutive odd integers whose sum equals 51, we can define the first integer as . org/ Detailed step by step solution for the sum of three consecutive integers is 51. Yes, the missing number is "9". Finding the Other Integers This was found by setting up the equation for the sum of three consecutive integers and solving for the middle integer. Before learning the formula for the sum of consecutive numbers, let’s recall what consecutive numbers are. Thus, 3x+6=108. - The second integer is . Now, in this section, we will learn about performing the addition of two or more than two consecutive numbers. . Sep 3, 2019 · Our three consecutive odd numbers are x, x + 2 and x + 4. What are the 4 integers?Practice this lesson yourself on KhanAcademy. Therefore, the three consecutive integers can be represented as x,x + 1, and x + 2. <br Sep 4, 2023 · To find the sum of 3 consecutive integers, we can set up an equation and solve it. asked • 09/16/20 Find 3 consecutive odd integers that have a sum of -51 Follow • 1 Add comment Report To find three consecutive integers that sum to 51, follow these steps: Thus, the three consecutive integers are 16, 17, and 18. Jan 28, 2025 · To solve for the greatest of three consecutive integers that sum up to -51, let's follow these steps: 1. Aug 17, 2021 · James D. Now, let's write the equation for their sum: x x x This simplifies to: x Next, we will subtract 6 from both sides: x Then, we divide both sides by 3: x Now that we have found , we can determine the three consecutive odd integers: First Consecutive integers are integers that follow each other in order. Sum of Consecutive Odd Integers Word Problems If you know how to solve word problems involving the sum of consecutive even integers, you should be able to easily solve word problems that involve the sum of consecutive odd integers. Ans: Hint: We are given that 3 consecutive odd integers are added to give -51, to find the number we must observe firstly that odd terms differ by 2. Click here 👆 to get an answer to your question ️ Find three consecutive odd integers that have the same sum of -51. The consecutive integers were represented as x, x+1, and x+2, leading to the solution -17. Determine the collective sum of three consecutive (even/odd) integers starting from a given integer using this straightforward calculator. Define the Integers: We'll let the three consecutive integers be represented as: - First integer: x - Second integer: x + 1 - Third integer: x + 2 2. The largest integer out of the three consecutive integers that sum to 51 is 18. they have a difference of One (1). What are the three numbers? Set up an equation where our numbers are n, n + 1, and n + 2 n + (n + 1) + (n + 2) = 153 Group variables and constants together: (n + n + n) + 1 + 2 = 153 3n + 3 = 153 Subtract 3 from each side: 3n + 3 - 3 = 153 - 3 Cancel the 3 on the left side and we get: 3n = 150 Divide each side of the equation by 3 to isolate n Dec 30, 2023 · Upload your school material for a more relevant answer The three consecutive integers that satisfy the condition are 52, 53, and 54. The consecutive integers are integers that follow each other in increasing order. Thus, we can create the equation: x+(x+1)+(x+2)=51 Combine like terms. Let the smallest integer be x. Dec 25, 2015 · If all three values were the middle value, divide the sum total (-45) by the sample size (3) to get the value of each number (-15). B)The quantity in Column B is greater. - The third integer is . What are these integers? 15,16,17 16,17,18 10,11,12 18,19,20 There are 3 consecutive integers that have a sum of 51 . What is the least of these integers? Submit Work it out Show More 100 Three consecutive integers have a sum of 51. The sum of 4 consecutive odd integers is 136. - brainly. Therefore, the other two consecutive integers can be expressed as x + 1 and x + 2. Explanation Three consecutive even integers can be represented by x, x+2, x+4. In this lesson, you will learn what are consecutive integers, and how to solve the kind of problems you are likely to come up against in tests, including: Finding the sum of two, three, or more consecutive integers Reversing that operation to find which consecutive integers sum up to a number There are also some examples to work through so you can get used to the method. Dec 21, 2014 · Consecutive integers are those numbers that follow each other continuously. Let's break the problem down: Define the integers: Let the first integer be x. Since the sum of three consecutive integers is given as 51 so, we will form the equation and find the value of x. So the three consecutive numbers are 16, 17 and 18. This is 17. The third number is 3 times the second. Now, the three consecutive integers will be 16, 17, and 18. Solving yields x = -17, confirming that the integers are -18, -17, and -16. For the numbers to be consecutive and have an average of 17, the middle number must be 17 and the two remaining numbers are 17-1 and 17+1 ie 16 and 18. Here’s the step-by-step approach: Write the equation. The sum of three consecutive integers equals 153. Dec 21, 2018 · Andrew B. Click here to get an answer to your question: Three consecutive integers have a sum of 51. The formula to add 'n' number of consecutive integers is: Sum of 'n' consecutive numbers= n/2 ( first . Sep 18, 2024 · An example of consecutive odd integers is {1, 3, 5} or {-3, -1, 1}. The relevant compound inequality is 51 \leq 3x + 3 \leq 72. what is the value of the middle number Sep 28, 2022 · To solve for the greatest of three consecutive integers whose sum is -51, let's denote the smallest integer as x. The sum of three consecutive odd integers is -51, how do you find the numbers?. The problem states that the sum of these three integers is 51. Our consecutive numbers lie around 17. Let the first integer be equal to x. Solve for : - Subtract 6 from both sides: - Divide both sides by 3: 5. Let's call the first integer n. Aug 28, 2024 · For instance, if you have three consecutive integers such as 1, 2, and 3, their sum would be 6. Consider a set of three consecutive integers: {–1, 0, +1}, here, multiple of 3 does not exist. Adding Consecutive Numbers Formula Introduction In mathematics, addition is a fundamental operation that involves combining two or more numbers to find their sum. Consecutive numbers are those numbers that differ by 1 which means, the difference between two consecutive numbers is always 1. Solving Word Problems that involve Consecutive Integers How to solve a word problem involving consecutive integers? Examples: Three consecutive integers have a sum of 78. The other two integers are x+1 and x+2. Detailed step by step solution for The sum of three consecutive integers is minus, 51−51. Detailed step by step solution for Three consecutive integers have a sum of 51. The smallest of these integers will be two less than 17 and the largest will be two more than 17, so the three consecutive odd integers will be 15, 17, and 19. We often encounter situations where we need to add a sequence of consecutive numbers, such as adding all the numbers from 1 to 20 or finding the sum of the first 100 positive integers. We found this by letting the first number be x, where x = 15, resulting in the numbers 15, 17, and 19. In the case of negative integers like -18, -17, and -16, their sum is also consistent with the integers being defined consecutively, in this case summing to -51. What are the three numbers? Set up an equation where our numbers are n, n + 1, and n + 2 n + (n + 1) + (n + 2) = 51 Group variables and constants together: (n + n + n) + 1 + 2 = 51 3n + 3 = 51 Subtract 3 from each side: 3n + 3 - 3 = 51 - 3 Cancel the 3 on the left side and we get: 3n = 48 Divide each side of the equation by 3 to isolate n Summary: If three consecutive integers add up to 51, the integers are 16, 17 and 18. Since we are looking for consecutive odd integers, the next two integers can be represented as follows: Sep 1, 2022 · What 3 consecutive integers have a sum of 51? Then also, the sum would be 51 and we would get the value of the number as 16, 17 and 18. Find the interges Your solution’s ready to go! Our expert help has broken down your problem into an easy-to-learn solution you can count on. As we get the one number x, we can easily calculate the other two numbers by substituting the value of x and hence get the desired result. Sep 16, 2020 · Algebra 1 Vanessa D. com Sep 5, 2024 · 3. No packages or subscriptions, pay only for the time you need. The three consecutive integers are 16, 17, and 18. Nov 9, 2017 · In general, if we want to look at any 3 consecutive integers starting with some integer n, the following integers will be n + 1 and n +2. Additionally, if we were to consider different sets of consecutive natural numbers, they would each yield different sums and may have different multiples of numbers like 13. The smallest of which is 15. Complete step-b Oct 2, 2024 · Answer: Let the three consecutive integers be , , and , where is the middle integer. The sum of three numbers is 116. From the above three examples, we can conclude an interesting fact that the product of any three consecutive integers, is always divisible by 6. Three consecutive integers starting with 7 would be 7, 8 and 9. Notice that, again, the difference between two adjacent numbers is always "two". Explai your reasoning. Aug 19, 2025 · To find three consecutive odd integers that have a sum of -51, we can follow these steps: Understanding Odd Integers: Odd integers are numbers that cannot be evenly divided by 2. Find the three consecutive odd integers: - The first integer is . The first integer is 16. Jan 7, 2015 · These three integers sum up to 51; therefore set up the following equation and solve: x+ (x+1)+ (x+2)=51 3x+3=51 3x=48 x=16 Therefore, the first integer is 16 and the next two integers are 17 and 18. The consecutive integers calculator will help you find the sequence of consecutive integers whose sum or product equals to the input value. If n is an odd integer, then n + 2, n + 4, and n + 6 are the consecutive odd integers. asked • 12/21/18 There are three consecutive integers. Please make sure to answer what the question asks for! Sep 28, 2022 · To find the greatest of three consecutive integers that sum to -51, we can set up the problem using a simple mathematical equation. Find these numbers. In this case, the sum of the integers is 48. According to the problem, their sum is -51, so we can write the equation as: n + (n + 1) + (n + 2) = 51 Simplify the equation: 3 n + 3 = 51 Subtract 3 from both sides: 3 n = 54 Finally, divide both sides by 3 to solve for n: n = 18 So, the three consecutive integers are 18, 17, 16. Sep 4, 2023 · The greatest of the three consecutive integers that sum to -51 is -16. Alternatively, 17, 19, and 21 would sum up to 57, also not equal to 51, confirming that 15, 17, and 19 is indeed the correct answer. To find the sum of consecutive numbers, a simple formula is used. In this case, we follow the same method of defining the first integer and continuing with increments of 2 to find the next integers. find the value of the greatest of the three Explanation To find the smallest of three consecutive odd integers with a sum of 51, we can set up an equation. Then the next two consecutive odd integers will be and . Their sum is -51. This is determined by setting the first integer as x, leading to the equations that ultimately solve for x. Dec 14, 2023 · A student has asked for the possible value of the first integer when three consecutive integers have a sum that is between 51 and 72. The second number is 6 less than the first. Oct 26, 2023 · To find the first of three consecutive integers whose sum is between 51 and 72 inclusive, set up a compound inequality and solve for the variable x. 00, # being the ones place) that add up to 11, 21, 31, 41, or 51 (if possible). Let the first integer be represented as x. To solve this, we can let the first integer be x, the second integer be x + 1, and the third integer be x + 2. This is calculated by setting the integers as x - 1, x, and x + 1, leading to the equation 3x = -51. Nov 25, 2024 · To find the largest integer among the three consecutive integers whose sum is 51, let's start by defining the three integers. Then the second and third integers will be equal to x + 1, x + 2. Apr 2, 2017 · What 3 consecutive integers have a sum of 51?Find an Online Tutor Now Choose an expert and meet online. Thus, the answer is correct and consistent with the problem's conditions. Adding these gives the total of 147 as required. Find their sum: The sum of these three consecutive integers is: x + (x + 1) + (x + 2) = 3x + 3 Set up the Dec 12, 2022 · First find the number which is 1/3 of 51. asked • 08/17/21 "An odd integer can be represented by the expression n + 2, where n is any odd integer. Three consecutive integers add up to 51. Final Answer The three consecutive integers that sum up to 51 are Free Sum of Three Consecutive Integers Calculator - Finds three consecutive integers, if applicable, who have a sum equal to a number. The consecutive integers formula helps in finding such integers for any given number or to check whether a set of integers are consecutive or not. <br /> The equation is x + (x + 2) + (x + 4) = 51. Feb 10, 2018 · Algebra Francesca C. The sum of three consecutive integers equals 51. If we represent one of these consecutive odd integers by the letter "n", then • the next odd consecutive integer will be represented by "n + 2" • the next consecutive odd integer beyond this will be "n + 4" and Nov 21, 2023 · One example of a sequence of consecutive integers is 1,2,3,4. We found this by defining the integers in terms of a variable and solving the resulting equation. Thus any three numbers which average 17 will always add up to 51. The sum of three consecutive odd numbers is 51. Three consecutive integers are such that when they are taken in increasing order and multiplied by 2, 3 and 4 respectively, they add up to 74. How to Find integers? The sum of three consecutive integers equals . Then we solve the equation for x. Steps to Solve Simplify the left side of the equation: 3x + 3 = 51 Subtract 3 from both sides to isolate 3x: 3x = 51 - 3 3x = 48 Divide both sides by 3 to solve for x: x = 48 / 3 x = 16 So, the three consecutive integers are 16, 17, and 18. Next, simplify the left side of the equation by combining like terms: x+x+1+x+ Transcript Question 6 Three Popular Examples The sum of two consecutive integers is −59. Set Up the Equation: According to the problem, the sum of these three integers is -51. So if we have n n as the first integer, then n + 1 n + 1 will be the second integer, n + 2 n + 2 will be the third integer, n + 3 n + 3 will be the fourth, n + 4 n + 4 will be the fifth, and so on. Dec 13, 2024 · To solve this problem, we need to find the first of three consecutive integers whose sum is between 51 and 72, inclusive. Next, find 3 consecutive numbers in the ones place (5#. <br /> Simplifying the equation, we get 3x + 6 = 51. Ideas for Solving the Problem Representation of Consecutive Integers: We can represent three consecutive integers as n, n+1, and n+2, where 'n' is the first integer. In these lessons, we will learn how to solve consecutive odd integer problems. org right now:https://www. 1. Jan 12, 2025 · To solve the problem of finding three consecutive integers where the sum of the first two is 51 more than the third integer, let's break it down step-by-step. Explore how to find consecutive integers, odd integers, or even integers that sum to a specific value using the Consecutive Calculator. Hence, we have again obtained the numbers as 16, 17 and 18. khanacademy. And since this arithmetic sequence has a constant difference of "2", simply add and subtract 2 from -15 to get: -15 + 2 = -13 -15 - 2 = -17 For example, if we take other sets of three consecutive odd integers such as 11, 13, and 15, their sum would be 39, which is not equal to 51. The integers are -18, -17, and -16. kx u3ff dzn3 pbt6 3sasqrvue kcv31z ukbymlg ozilh 5goo 9fqv