geometric series worksheet solution1

Geometric Series Worksheet Solution1

In the page geometric series worksheet solution1 you are going to see solution of each questions from the geometric series worksheet.

(1) Find the sum of first 20 terms of the geometric series

5/2 + 5/6 + 5/18 + ............

Solution:

To find the sum of first 20 terms of the geometric series first we have to find the value of r. Then only we can decide which formula should be used in this problem.

r = t₂/t₁ a = 5/2 and n = 20

r = (5/6)/(5/2)

= (5/6) x (2/5)

r = 1/3 here r < 1

s_n = a(1- rⁿ)⁄(1 - r)

So, S₂₀ = (5/2) [1- (1/3)^₂₀]/[1-(1/3)]

= (5/2) [1- (1/3)^₂₀]/[2/3]

= (5/2) x (3/2) [1- (1/3)^₂₀]

= (15/4) [1 - (1/3)^₂₀]

(2) Find the sum of first 27 terms of the geometric series 1/9 + 1/27 + 1/81 + ............

Solution:

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

s_n = 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

s_n = a( rⁿ - 1 )⁄( r - 1)

S₈ = 3 (2⁸ - 1)/(2-1)

S₈ = 3 (256 - 1)/(1)

S₈ = 3 (255)

S₈ = 765