Find the sum of a geometric series. 20 - 5 + 5/4 - 5/16 + ... A) 220/7 B) 16 C) 286/13 D) 66

Question

asked May 26, 2021 196k views

2 Answers

Butters · Answer 1 · 2021-05-30T20:08:21+0000

Answer:

Option B.

Explanation:

Consider the given geometric series is

S=20-5+(5)/(4)-(5)/(16)+...

We need to find the sum of given series.

Here, first term is a=20 and common ratio is

r=(-5)/(20)=-(1)/(4)

The sum of infinite GP is

S=(a)/(1-r)

Substitute
$a=20\text{ and }r=(-5)/(20)=-(1)/(4)$ .

S=(20)/(1-(-(1)/(4)))

S=(20)/((5)/(4))

S=(20* 4)/(5)

S=16

Therefore, the correct option is B.