Geometric Sequence Worksheet Solution2





In the page geometric sequence worksheet solution2 you are going to see solution of each questions from the geometric series worksheet.

(3) If the 4th and 7th terms of a G.P are 54 and 1458 respectively,find the G.P

Solution:

   4th term = 54

  7th term = 1458

       t₄ = 54

       a r³ = 54   ----- (1)

       t₇ = 1458

      a r⁶ = 1458  ----- (2)

(2)/(1) = (a r⁶)/(a r³) = 1458/54

                        r³ = 27

                        r³ = 3³

                        r = 3

Substitute r = 3 in the first equation we get 

                    a (3)³ = 54

                    a(27) = 54 

                       a = 54/27

                       a = 2  


The general form of G.P is   a, a r , a r ²,.........

               = 2 ,2(3),2(3)²,..............

               = 2,6,18,............


(4) In a geometric sequence, the first term is 1/3 and the sixth term is 1/729,find the G.P

Solution:

  first term = 1/3

  6th term = 1/729

       a = 1/3

       t₆ = 1/729

      a r⁵ = 1/729

applying the value of a in this equation we get

         (1/3) r⁵ = 1/729

                 r⁵ = (1/729)/(1/3)

                 r⁵ = (1/729)x(3/1)

                 r⁵ = 1/243

                 r⁵ = (1/3)⁵

                 r = 1/3

The general form of G.P is   a, a r , a r ²,.........

               = 1/3 ,(1/3)(1/3),(1/3)(1/3)²,..............

               = 1/3,1/9,1/27,............


(5) Which term of the geometric sequence

(i) 5,2,4/5,8/25,...............is 128/15625?

Solution:

we do not know which term is 128/15625.So let us consider 128/15625 as nth term of the sequence

               so      tn = 128/15625

                ar^(n-1) =  128/15625

     a = 5      r = 2/5

                 5 (2/5)^(n-1) = 128/15625

                   (2/5)^(n-1) = 128/(15625 x 5)

                   (2/5)^(n-1) = 2⁷/(5⁶ x 5)       

                   (2/5)^(n-1) = 2⁷/5⁷

                   (2/5)^(n-1) = (2/5)⁷

                            n - 1 = 7

                               n = 7 + 1

                               n = 8

From this calculation we come to know that 8th term of the given sequence is 128/15625.


(ii) 1,2,4,8,..........is 1024?

Solution:

we do not know which term is 1024.So let us consider 1024 as nth term of the sequence

               so      tn = 1024

                ar^(n-1) =  1024

     a = 1      r = 2/1

                  r = 2 

                 1 (2)^(n-1) = 1024

                   (2)^(n-1) = 2^10

                            n - 1 = 10

                               n = 10 + 1

                               n = 11

From this calculation we come to know that 11th term of the given sequence is 1024.

you can get solution for remaining question in the next page.geometric sequence worksheet solution2 geometric sequence worksheet solution2