Geometric Progression Formula:

The geometric progression formula is given below.

The general form of a geometric progression (GP) is a, ar, ar², ar³, ... 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-rⁿ| / |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 , t₅ = a r^5-1 = a r⁴

t₅ = 64(1/4)⁴ = 64/256 = 1/4

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

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