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Geometric Sequence Formula

A geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed.

The Geometric Sequence Formula is given as,

\[\large g_{n}=g_{1}\;r^{n-1}\]

Where,
gn – nth term that has to be found
g1 – 1st term in the series
r – common ratio

Solved Examples

Question 1: Find the 9th term in the arithmetic sequence 2, 14, 98, 686,…. ?

Solution:

The geometric sequence is given as,
gn = g1 $\times$ r(n – 1)

From the given problem,
g1 = 2 ; n = 9 ; r = 7
g9 = 2 $\times$ 7(9 – 1)
g9 = 2 $\times$ 78
g9 = 2 $\times$ 5764801
g9 = 11529602

More topics in Geometric Sequence Formula
Infinite Geometric Series Formula Geometric Series Formula