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Question

Find 12th term of a GP, whose 8th term is 192 and common ratio is 2 .


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Solution

Step 1. Find the first term of GP:

We know that nth term of a G.P. is given as
an=arn-1
Where an=nth term of the G.P., n is the number of terms, a is the first term, and r is the common ratio.

Here, common ratio, r=2.

8th term a8=192
a(2)8-1=192a(2)7=192a×128=192a=192128a=32

Therefore, the first term of GP is a=32.

Step 2: Find 12th term of a GP:

a12=ar12-1=32×211=32×2048=3×1024=3072

Hence, the value of 12th term of the G.P. is 3072.


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