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, ar^{2}, ar^{3}, ar^{4}, ................, ar^{n - 1}
That is, T_{1} = a
T_{2} = ar
T_{3} = ar^{2}
: : : :
T_{n} = ar^{n - 1}
This is similar to A.P. We take an example to become more familiar with this.
Example
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
T_{1} = a = 3
T_{2} = ar = 3.2 = 6
T_{3} = ar^{2} = 3.2.2 = 12
The nth term is given by T_{n} = ar^{n-1} = 3(2)^{n-1}