GEOMETRIC PROGRESSION

Example 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 :

t₁  =  0.12, t₂  =   0.24 and t₃  =  0.48

Since the common ratios are same, the given sequence is geometric progression.

The required common ratio is 2.

(ii)  0.004, 0.02, 1, ..........

Solution :

t₁  =  0.004, t₂  =   0.02 and t₃  =  1

Since the common ratios are not same, the given sequence is not a geometric progression.

The required common ratio is 5.

Example 2 :

Find the  10^th term and the common ratio of the geometric sequence

1/4, -1/2, 1, -2,............

Solution :

To find the 10^th terms of the G.P we use the formula given below.

t_n = a r^(n-1)

a  =  1/4,  r = (-1/2) / (1/4) ==> -2 and n = 10   

t₁₀  =  (1/4) (-2)^{(10 - 1)}

t₁₀  =  (1/4) (-2)⁹

t₁₀  =  (1/4) (-512)

t₁₀  =  -128

Therefore the 10^th and common ratio of the given geometric sequence are -128 and -2 respectively.

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