Question

The sum to infinity of a convergent geometric series with a common ratio r is S. Given that S=200 and the sum of the first 3 terms is 175
(a) find the value of r.

Given also that Sn/S = 255/256
(b) find the value of n.

Answer 1

Answer:

(a) 1/2

(b) 8

Step-by-step explanation:

(a)

S = a/(1-r); for convergent infinite series of GP

=> 200=a/(1-r)-----(1)

also given that, a+ar+ar² = 175----(2)

solving (1) & (2)

r = 1/2

and a =100

(b)

Sn = a(1-rⁿ)/(1-r)

given that, Sn/S= 255/256

[100(1-1/2ⁿ)/(1-1/2)]/200= 255/256

1-1/2ⁿ=255/256

1/2ⁿ=1/256

2ⁿ=256=2⁸

n=8