The geometric progression formula is given below.

The general form of a geometric progression (GP) is a, ar, ar^{2}, ar^{3}, ... with a ≠ 0 and C.R = r ≠ 0

1. The n^{th }term of the G.P is t_{n} = ar^{n–1}

2. Sum of the first n terms in a G.P. S_{n }= a|1-r^{n}| / |1-r|

example:

Find the 5^{th }term of the G.P 64, 16, 4...

**Solution:**

a = 64, r =16 /64= 1/ 4, n = 5

t_{n} = a r^{n-1} , t_{5} = a r^{5-1} = a r^{4}

t_{5} = 64(1/4)^{4} = 64/256 = 1/4

5^{th} term of the given geometric progression is 1/4.

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