Question

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

Answer 1

Answer:

$S_{8}$ = - 536

Step-by-step 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

$S_{n}$ = $\frac{n}{2}$ [ 2a₁ + (n - 1)d ] , thus

$S_{8}$ = $\frac{8}{2}$ [ (2 × 10) + (- 154) ]

    = 4(20 - 154)

    = 4 × - 134

    = - 536