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31 July, 03:42

The sum of 6 consecutive integers is 597

What is the 3rd number in this sequence?

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  1. 31 July, 03:52
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    First represent your 6 consecutive integers as follows.

    X ⇒ first integer

    X + 1 ⇒ second integer

    X + 2 ⇒ third integer

    X + 3 ⇒ fourth integer

    X + 4 ⇒ fifth integer

    X + 5 ⇒ sixth integer

    Since their sum is 597, our equation reads

    x + (x + 1) + (x + 2) + (x + 3) + (x + 4) + (x + 5) = 597.

    Simplifying on the left we get 6x + 15 = 597.

    Now subtract 15 from both sides to get 6x = 582.

    Now dividing both sides by 6, we find that x = 97.

    So our first integer, x, is 97.

    Our third integer would be x + 2 or 97 + 2 which is 99.
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