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Q: Find four consecutive integers whose sum is 114?

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The answer to that question is 6,7,8,9.

The numbers are 82, 84, 86 and 88.

The integers are 26, 27, 28 and 29.

19, 20,21,22

The integers are 81, 83, 85 and 87.

They are odd consecutive integers: 21, 23, 25 and 27.

There is a set of four consecutive even integers whose sum is four. The set is: -2, 0, 2 and 4.

58, 60, 62, 64

11, 13, 15, and 17

101, 103, 105, 107

There are four consecutive odd integers: 81, 83, 85 and 87.

6,7,8,9

15,16,17,18

The integers are 21, 22, 23 and 24.

The integers are 6, 7, 8 and 9.

No.

27 + 28 + 29 + 30 = 114

The integers are -2, 0, 2 and 4.

The integers are 17, 19, 21 and 23.

1,2,3,4

-4, -2, 0, and 2 are the four consecutive even integers. When you add them up they equal -4.

24 + 25 + 26 + 27 = 102

There are none. The only four consecutive integers totaling 90 are 21, 22, 23 and 24.

This is not possible. Four odd integers, consecutive or otherwise, MUST total an even number eg 5 + 7 + 9 + 11 = 32

The average of the four numbers will be equal to 116/4 = 29 Since you are looking for an even number of integers, you cannot have them averaging an odd number.