Question

The second term of a G.P. is 12 more than
the first term, given that the common ratio is
half of the first term. Find the third term of the
G.P.​

Answer 1

Step-by-step explanation:

Consider a G.P series where first term is 'a' and common difference is 'r'

Let the series be a, ar,ar^2,ar^3 and so on..

3rd term=12=ar^2

6th term=96=ar^5

Dividing ar^5/ar^2, we get r^3=8=2^3

Therefore r=2

And, a=3

The terms are: 3,6,12,24,48,96,192,384,768…. and so on

For finding the sum of the terms we use the formula, s=a*(1-r^n)/(1-r), where n is the number of terms

Therefore, s=3*(1–2^9)/(1–2)=1533