find the sum of the first 27 terms of geometric series 1/9+1/27+1/81+. .....
Answers
To find the sum of first 27 terms of the geometric series first we have to find the value of r. Then only we can decide which formula to be used in this problem.
r = t₂/t₁ a = 1/9 and n = 27
r = (1/27)/(1/9)
= (1/27) x (1/9)
r = 1/3 here r < 1
sn = a(1- rn)⁄(1 - r)So, S₂₇ = (1/9) [1- (1/3)^₂₇]/[1-(1/3)]
= (1/9) [1- (1/3)^₂₇]/[2/3]
= (1/9) x (3/2) [1- (1/3)^₂₇]
= (1/6) [1 - (1/3)^₂₇]
(3) Find the sum of n terms of the geometric series described below
(i) a = 3,t₈ = 384,n=8
Solution:
To find the sum of first 8 terms of the geometric series first we have to find the value of common ratio that is r. Then only we can decide which formula to be used in this problem.
t₈ = 384
ar⁷ = 384
(3) r⁷ = 384
r⁷ = 384/3
r⁷ = 128
r⁷ = 2⁷
r = 2 >1
S₈ = 3 (2⁸ - 1)/(2-1)
S₈ = 3 (256 - 1)/(1)
S₈ = 3 (255)
S₈ = 765