First represent your 6 consecutive integers as follows.
X ⇒ <em>first integer</em>
X + 1 ⇒ <em>second integer</em>
X + 2 ⇒ <em>third integer</em>
X + 3 ⇒ <em>fourth integer</em>
X + 4 ⇒ <em>fifth integer</em>
X + 5 ⇒ <em>sixth integer </em>
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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 <em>x = 97</em>.
So our first integer, x, is 97.
Our third integer would be x + 2 or 97 + 2 which is 99.