The third term of a G.P. is 4, the product of the first five terms

Question:

The third term of a G.P. is 4, the product of the first five terms is ____________.

Solution:

Given third term of G.P is 4

Let a be the first term of G.P and r denote the common ratio.

Then second term is ar

Third term is ar2

fourth term is ar3 and fifth term is ar4 .

Since ar2 = 4

Product of first 5 terms is aarar2 ar3 ar4

a5 r10

= (ar2)5

Hence, product of first 5 terms = 45

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