Question

Consecutive numbers are whole numbers that follow in order such as 7, 8, 9, 10, and so forth. Suppose the average of 15 consecutive numbers is 15. What is the average of the first five numbers of the set?

Answer 1

10

Explanation:

First, we need to find the sum of the 15 consecutive numbers. The formula to finding the average of a set of numbers is the sum of the terms divided by the number of terms. So to find the sum, you do 15x15 because the average is 15 and there are 15 numbers. 15x15=225, so you know the sum of the consecutive numbers is 225. Let X be equal to the first consecutive number of the 15 consecutive numbers.

X+(X+1)+(X+2)+(X+3)....+(X+14)=225

=15X+(105)=225

=15X=225-105

=15X=120

=X=8

So the first consecutive number of the 15 is 8. Therefore, the second consecutive number is 9, the third is 10, and so on. The question asks for the average of the first five numbers, which is 8, 9, 10, 11, and 12.

The summation formula is
`S=(\alpha_(1)+\alpha_(n))(n)/(2\\)`.

`S=(\alpha_(1)+\alpha_(n))(n)/(2\\)\\ S=(8+12)(5)/(2)\\ S=(20)2.5\\ S=50`

So the sum of the first five consecutive numbers is 50. Since there are 5 numbers, you do 50÷5=10. Therefore, the answer is 10.