Question

(can i get a step by step answer)

determine the sum of the arithmetic series
8 + 3 - 2 - ... - 102

Answer 1

- 1081

Explanation:

We require the number of terms in the series.

The n th term of an arithmetic sequence is

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

where a is the first term and d the common difference

d = 3 - 8 = - 5 and a = 8, thus

8 - 5(n - 1) = - 102 ← the last term in the series

8 - 5n + 5 = - 102

13 - 5n = - 102 ( subtract 13 from both sides )

- 5n = - 115 ( divide both sides by - 5 )

n = 23 ← number of terms in series

The sum to n terms is calculated as

`S_(n)` =
`(n)/(2)` (first term + last term )

The first term = 8 and the last term = - 102, thus

`S_(23)` =
`(23)/(2)` (8 - 102) = 11.5 × - 94 = - 1081