Question

I need help ASAP PLEASE

What is the sum of the first 47 terms of the sequence?
-215,-201,-187,-173,...

Answer 1

5029

Explanation:

There is a common difference between consecutive terms, that is

d = - 201 - (- 215) = - 187 - (- 201) = - 173 - (- 187) = 14

This indicates the sequence is arithmetic with sum to n term

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

where a₁ is the first term and d the common difference

Here a₁ = - 215 and d = 14 , then

`S_(47)` =
`(47)/(2)` [ (2 × - 215) + (46 × 14) ]

= 23.5 (- 430 + 644)

= 23.5 × 214

= 5029