Find the sum of the first 90 terms of the sequence -4,-1,2,5,8

Question

asked Feb 2, 2021 65.4k views

2 Answers

Kathy Judd · Answer 1 · 2021-02-06T20:53:02+0000

Answer:

1655

Explanation:

Note the common difference d between consecutive terms of the sequence

d = - 1 - (- 4) = 2 - (- 1) = 5 - 2 = 8 - 5 = 3

This indicates the sequence is arithmetic with sum to n terms

S_(n) =
(n)/(2) [ 2a₁ + (n - 1)d ]

Here a₁ = - 4, d = 3 and n = 90, thus

S_(90) =
(90)/(2) [ (2 × - 4) + (89 × 3) ] = 45(- 8 + 267) = 45 × 259 = 1655