Learning geometric progression vis-á-vis arithmetic progression should make it easier. In geometric progression also we denote the first term by 'a' but a basic difference from A.P. is that instead of common difference we have common ratio 'r'. Like d, r remains constant whenever the ratio of any two consecutive terms is computed. The terms of a G.P. are
a, ar, ar2, ar3, ar4, ................, arn - 1
That is, T1 = a
T2 = ar
T3 = ar2
: : : :
Tn = arn - 1
This is similar to A.P. We take an example to become more familiar with this.
It is known that the first term in G.P. is 3 and the common ratio r is 2. Find the first three terms of this series and also the nth term.
We know that the first term is given by
T1 = a = 3
T2 = ar = 3.2 = 6
T3 = ar2 = 3.2.2 = 12
The nth term is given by Tn = arn-1 = 3(2)n-1