# If the 4th and 9th terms of a G.P. be 54 and 13122 respectively, find the G.P.

## Solution :

Let a be the first term and r the common ratio of the given G.P. Then,

$$a_4$$ = 54  and  $$a_9$$ = 13122

$$\implies$$  $$ar^3$$ = 54   and  $$ar^8$$  =  13122

$$\implies$$  $$ar^8\over ar^3$$ = $$13122\over 54$$  $$\implies$$  $$r^5$$ = 245  $$\implies$$  r = 3

Putting r = 3 in $$ar^3$$ = 54,

we get a = 2.

Hence, the given G.P is 2, 6, 18, 54, ….

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