Question

Find S8 for the arithmetic series 10+ ...-144.

Answer 1

`S_(8)` = - 536

Explanation:

The n th term of an arithmetic series is

`a_(n)` = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Here a₁ = 10 and
`a_(n)` = - 144 , thus

10 + (n - 1)d = - 144 ( subtract 10 from both sides )

(n - 1)d = - 154

The sum to n terms of an arithmetic series is

`S_(n)` =
`(n)/(2)` [ 2a₁ + (n - 1)d ] , thus

`S_(8)` =
`(8)/(2)` [ (2 × 10) + (- 154) ]

= 4(20 - 154)

= 4 × - 134

= - 536