This document provides guidance on solving problems involving finding the sum of consecutive integers. It explains that you need to determine the number of integers being summed and whether they are consecutive evens, odds, or neither. It then demonstrates applying the appropriate formula - adding 1 or 2 to each successive integer - to set up and solve example problems finding sets of consecutive integers whose sum equals a given value.

1. Sum of Consecutive Integers
● Problems ask for the sum of consecutive integers.
● You need to figure out 2 things
○ How many consecutive integers - May be 2 integers,
may be 3 integers.
○ Type: Consecutive Even, consecutive odd, or
consecutive
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2. Sum of Consecutive Integers Approach
● Start with a number n
● If even or odd, add 2 to each number
○ n, n + 2, n + 4
● If not even or odd, add 1 to each number
○ n, n + 1, n + 2
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3. Sum of Consecutive Integers Example
Sum of 3 consecutive integers equals 27. What
are the integers?
Because no odd or even stated, we add 1.
n + (n + 1) + (n + 2) = 30
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4. Sum of Consecutive Integers Example Part 2
n + (n + 1) + (n + 2) = 30
Group like terms, variables and constants:
(n + n + n) + (1 + 2) = 30
3n + 3 = 30
3n = 27
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5. Sum of Consecutive Integers Example Part 3
3n = 27
Divide each side by 3. n = 9.
Which means n + 1 = 9 + 1 = 10
n + 2 = 9 + 2 = 11
(9, 10, 11)
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6. Sum of Consecutive Even Integers Example
Sum of 3 consecutive even integers equals 30.
What are the integers?
Because we said even, we add 2.
n + (n + 2) + (n + 4) = 30
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7. Sum of Consecutive Even Integers Example Part 2
n + (n + 2) + (n + 4) = 30
Group like terms, variables and constants:
(n + n + n) + (2 + 4) = 30
3n + 6 = 30
3n = 24
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8. Sum of Consecutive Even Integers Example Part 3
3n = 24
Divide each side by 3. n = 8.
Which means n + 2 = 8 + 2 = 10
n + 4 = 8 + 4 = 12
(8, 10, 12)
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9. Sum of Consecutive Integers Calculator
https://www.mathcelebrity.com/calculator.php
Sum of 3 consecutive integers equals 27
Sum of 3 consecutive even integers is 30
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