The sum of 3 consecutive integers is 261. What is the middle number?

Let us assume the smallest integer = x

Then the middle integer = x + 1

The biggest integer among the three consecutive integers = x + 2

It is also given in the question that the sum of the three consecutive integers is 261.

Then

x + x + 1 + x + 2 = 261

3x + 3 = 261

3x = 261 - 3

3x = 258

x = 258/3

= 86

Then

The middle integer = x + 1

= 86 + 1

= 87

So from the above deduction we can easily see that the middle integer is 87.