Geometric Sequence Formula

The geometric sequence formula refers to determining the n^th term of a geometric sequence. To recall, a geometric sequence or a geometric progression is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed.

Formula for Geometric Sequence

The Geometric Sequence Formula is given as,

Where,

• g_n is the n^th term that has to be found
• g₁ is the 1^st term in the series
• r is the common ratio

Try This: Geometric Sequence Calculator

Solved Example Using Geometric Sequence Formula

Question 1: Find the 9^th term in the geometric sequence 2, 14, 98, 686,…

Solution:

The geometric sequence formula is given as,
g_n = g₁ × r^{(n – 1)}

From the given problem,
g₁ = 2 ; n = 9 ; r = 7
g₉ = 2 × 7^{(9 – 1)}
g₉ = 2 × 7⁸
g₉ = 2 × 5764801
g₉ = 11529602

Therefore, the 9th term of the sequence is 11529602.