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

sn = 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

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 

sn = a( rn - 1 )⁄( r - 1)

        S₈ = 3 (2⁸ - 1)/(2-1)

        S₈ = 3 (256 - 1)/(1)

        S₈ = 3 (255)

          S₈ = 765


(ii)    a = 5,r = 3,n=12 

Solution:

We have to find the sum of first 12 terms of the geometric series here the common ratio is 3 > 1.

sn = a( rn - 1 )⁄( r - 1)

        S₁₂ = 5 (3¹² - 1)/(3-1)

        S₁₂ = 5 (3¹² - 1)/(2)

        S₁₂ = (5/2) (3¹² - 1)

          S₁₂ = (5/2) (3¹² - 1)

These are the contents in the page geometric series worksheet solution1.



geometric series worksheet solution1