7) Find five consecutive integers such that the sum of the first three numbers equals 2 times the fifth number.

Explanation:

Consecutive integers are ones that follow one right after another. Some examples include:

We don't know what the starting value is, so let's say its x. The next number after that is x+1. Then after that is (x+1)+1 = x+2. And so on.

The sum of the first three terms is equal to twice the fifth number, so,

(first) + (second) + (third) = 2(fifth)

(x) + (x+1) + (x+2) = 2(x+4)

3x+3 = 2x+8

3x-2x = 8-3

x = 5

The starting item is 5. The next is 6 and so on.

The five numbers are: 5,6,7,8,9

Check:

Summing the first three terms = 5+6+7 = 11+7 = 18

Twice the fifth term = 2*9 = 18

The answer is confirmed.

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step-by-step explanation:

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