Question

Find the sum of this arithmetic series.
| 26 + 24.5 + 23 + 21.5 + ... - 17.5

Answer 1

127.5

Explanation:

The given series is 26 + 24.5 + 23 + 21.5 + ... - 17.5

The first term of this series is a=26

The common difference is d=24.5-26=-1.5

The last term of the series is -17.5

The nth term is given by:

`u_n=a+d(n-1)`

`26+-1.5(n-1)=-17.5`

`-1.5n=-17.5-26-1.5`

`-1.5n=-45`

n=30

The sum of the series:

`S_(n)=(n)/(2)(a+l)`

`S_(30)=(30)/(2)(26+-17.5)`

`S_(30)=127.5`