Geometric Sequence Worksheet Solution1





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

(1) Find out which of the following sequences are geometric sequences . For those geometric sequences,find the common ratio.

(i) 0.12,0.24,0.48,.........

Solution:

A sequence is said to be a Geometric progression if the ratio of each term,except the first one to its proceeding is always by a constant.Now let us check whether the ratio is same or not .For that we have to divide the second term by first term,and third term by second term.If we get the same answer in both ways we can say the given sequence is G.P otherwise it is not G.P

       r = 0.24/0.12                 r = 0.48/0.24

         =  2                              = 2

In both ways we get the same answer.So we can decide the given sequence is G.P and the common ratio (r) is 2.


(ii) 0.004,0.02,0.1,..........

Solution:

          r = 0.02/0.004                  r = 0.1/0.02

            = 5                                 = 5

In both ways we get the same answer.So we can decide the given sequence is G.P and the common ratio (r) is 5.


(iii) 1/2,1/3,2/9,4/47,...........

Solution:

          r = (1/3)/(1/2)                  r = (2/9)/(1/3)

          r = (1/3)x(2/1)                  r = (2/9)x(3/1)

             = 2/3                              = 2/3

In both ways we get the same answer.So we can decide the given sequence is G.P and the common ratio (r) is 2/3.

(iv) 12,1,1/12,............

Solution:

          r = 1/12                           r = (1/12)/(1)

             = 1/12                             = 1/12

In both ways we get the same answer.So we can decide the given sequence is G.P and the common ratio (r) is 1/12.


(v) √2,1/√2,1/(2√2),...........

Solution:

          r = (1/√2)/√2                           r = (1/2√2)/(1/√2)

             = 1/2                                      = (1/2√2) x (√2/1)

                                                          = 1/2

In both ways we get the same answer.So we can decide the given sequence is G.P and the common ratio (r) is 1/2.

(vi) 4,-2,-1,-1/2,...............

Solution:

          r = -2/4                           r = (-1)/(-2)

             = -1/2                             = 1/2

In both ways we don't get the same answer.So we can decide the given sequence is not  G.P.


(2) Find the  10th term and the common ratio of the geometric sequence 1/4,-1/2,1,-2,............

Solution:

To find the 10th terms of the G.P we have to use the formula for general term that is

                  tn = a r^(n-1)

         here a = 1/4   r = (-1/2)/(1/4)          n = 10   

                               = (-1/2) x (4/1)

                               = -2

                   t₁₀ = (1/4) (-2)^(10-1)

                       = (1/4) (-2)^9

                       = (1/4) (-512)

                       = -512/4

                       = -128  



geometric sequence worksheet solution1 geometric sequence worksheet solution1