Question

The sum of 5 consecutive integers is 265. What is the fifth number in this sequence?

Answer 1

Five consecutive integers are:

n, n+1, n+2, n+3, n+4  the sum of which is:

5n+10=265  subtract 10 from both sides

5n=255, divide both sides by 5

n=51

Our fifth number was n+4 so the fifth number is 55

Answer 2

Let x = the first consecutive number
Then x + 1 = the second consecutive number
Then x + 2 = the third consecutive number
Then x + 3 = the fourth consecutive number
Then x + 4 = the fifth consecutive number

The sum of the 5 consecutive integers is 265

x + x + 1 + x + 2 + x + 3 + x + 4 = 265

Combine like terms.

5x + 10 = 265

Solve for x.

5x + 10 = 265
5x = 255 <-- Subtract 10 from each side
x = 51 <-- Divide both sides by 5

So, the fifth consecutive integer is 51 + 4 or 55.