Question

What is the sum of the first 43 terms of the sequence? −235,−217,−199,−181,...

Answer 1

S₄₃ = 6149

Explanation:

there is a common difference between consecutive terms in the sequence, that is

- 217 - (- 235) = - 217 + 235 = 18

- 199 - (- 217) = - 199 + 217 = 18

- 181 - (- 199) = - 181 + 199 = 18

This indicates the sequence is arithmetic with

sum to n terms

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

a₁ is the first term, d the common difference , n the term number

here a₁ = - 235 , d = 18 and n = 43 , then

S₄₃ =
`(43)/(2)` [ (2 × - 235) + (42 × 18) ]

= 21.5 ( - 470 + 756 )

= 21.5 × 286

= 6149