The sum of 6 consecutive integers is 597

What is the 3rd number in this sequence?

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.