Question

The sum of 5 consecutive integers is 505. What is the second number in this sequence?

Answer 1

The second number is 100.

Explanation:

Let the first integer be x.

Then since the five integers are consecutive, the second integer will be (x + 1), the third (x + 2), fourth (x + 3), and the fifth (x + 4).

They total 505. Hence:

`\displaystyle x+(x+1)+(x+2)+(x+3)+(x+4)=505`

Solve for x. Combine like terms:

`5x+10=505`

Subtract 10 from both sides:

`5x=495`

And divide both sides by five. Hence:

`x=99`

Thus, our sequence is 99, 100, 101, 102, and 103.

The second number is 100.