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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