Question

Find the sum of this series: 91 + 78 + 65 + 52 + …; 20th term.

A. −650
B. −1300
C. −780
D. −1160

Answer 1

A

Explanation:

there is a common difference between consecutive terms , that is

78 - 91 = 65 - 78 = 52 - 65 = - 13

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 = 91 , d = - 13 and n = 20 , then

S₂₀ =
`(20)/(2)` [ ( 2 × 91) + (19 × - 13) ]

= 10 (182 + (- 247))

= 10(182 - 247)

= 10 × - 65

= - 650