Question

Given the series below, find S29.

{13+4+(−5)+(−14)+(−23)+...}

Select one:
a. -2,480
b. -2,752
c. -3,016
d. -3,277

Answer 1

d

Explanation:

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

4 - 13 = - 5 - 4 = - 14 - (- 5) = - 23 - (- 14) = - 9

this indicates the series is arithmetic with sum to n terms

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

where a₁ is the first term and d the common difference

here a₁ = 13 and d = - 9 , then

S₂₉ =
`(29)/(2)` [ (2 × 13) + (28 × - 9) ]

= 14.4(26 + (- 252))

= 14.5(26 - 252)

= 14.5 × - 226

= - 3,277