Question

Find the sum of the first 32 terms of the arithmetic sequence 24, 20, 16,

Answer 1

`S_(32)` = - 1216

Explanation:

The sum to n terms of an arithmetic sequence is

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

where a₁ is the first term and d the common difference

Here a₁ = 24 and d = a₂ - a₁ = 20 - 24 = - 4 , then

`S_(32)` =
`(32)/(2)` [ (2 × 24) + (31 × - 4) ]

= 16(48 - 124)

= 16 × - 76

= - 1216