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How many terms of G.P. 3, 32, 33, … are needed to give the sum 120?

Given G.P. is

How about we consider that

   

terms of this G.P. be needed to acquire the amount of

   

We realize that,

Here,

   

Equating the types we get,

   

Hence, four terms of the given

   

are needed to acquire the total as