**GEOMETRIC PROGRESSION (G.P.)**

A G.P. is a sequence whose first term is non-zero and each of whose succeeding term is r times the preceding term, where r is some fixed non – zero number, known as the common ratio of

the G.P. For example 3 + 9 + 27 + 81 is a G.P. whose common ratio is 3.

**n ^{th} Term and Sum of n Terms:**

If a is the first term and r the common ratio, then G.P. can be written as a, ar, ar^{2}, . . . the nth term, a_{n}, is given by a_{n} = ar^{n-1}. The sum S_{n} of the first n terms of the G.P. is

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