Question

(1) Find the 10th and nth term of the G.P 5, 25, 125 .......

(2) Which term of G.P ...2, 8, 32 .....up to n terms is 131072 ?

(3)In G.P the 3rd term is 24 and the 6th term is 192 . find the 10th term.

Answer 1

Solution :- (1) Here a = 5 and r = 5 ,this a10 = 5 ( 5)^10 - 1 = 5 (5)^9 = 5^10 and

an = ar^n-1 = 5 ( 5) ^n - 1 = 5^n

Solution:- (2) Let 131072= an = 2(4)^n - 1

or 65536 = 4^n -1

this , gives 4^8 = 4^n - 1

so that n- 1 = 8 , i.e .., n = 9 . Hence, 131072 is the 9th term of the G.P

Solution :- (3) Here, a3 = ar² = 192
and, a6 = ar^5 = 192

Dividing (2) by (1) we get r = 2 , substituting r = 2 in (1) , we get a = 6

Hence, a10 = 6 (2)^9 = 3072 answer ..

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