Question

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

Answer 1

Answer:

127.5

Step-by-step 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:

$S_{n}=\frac{n}{2}(a+l)$

$S_{30}=\frac{30}{2}(26+-17.5)$

$S_{30}=127.5$