=>        n - 1 / 2 = 6

Therefore; n = 13.

Hence 128 is the 13^th term of the GP.

Example - 22.In a GP the 3rd term is 24 and 6th term is 192. Find the 10th term

Solution:Here        a₃ = ar² = 24        ...(1)

a₆ = ar⁵ = 192       ...(2)

Dividing (2) by (1) we get ar ^ 5 / ar ^ 2) = 192/24

=> r³ = 8 = 2³

=> r = 2

Substituting r = 2 in (1) we get a = 6.

Therefore ; a₁₀ = ar ^ 9 = 6(2) ^ 9 = 3072 .

Exercise - 6.5

1. For each geometric progression find the common ratio 'r', and then find a_n

(i) 3, 3/2 , 3/4 , 3/8....       (ii) 2.-6, 18.-54

(iii) -1 , -3 , -9 , -27...       (iv) 5 , 2 , 4/5 , 8/25...

2. Find the 10th and n ^th term of GP. : 5, 25, 125, ....

3 . Find the indicated term of each Geometric Progression.

(i).a₁ = 9; r = 1/3 find a₇       (ii) a₁ = - 12; r = 1/3 ;find a₆

4 . Which term of the GP.

i) 2, 8, 32, is 512 ?       (ii)  3, 3 ,3 √3.....is 729?

iii)1 / 3, 1 / 9 , 1 / 27 .....is 1 / 2187?