Geometric Sequence Formula

Geometric Sequence formula simply indicates finding the nth term of a geometric sequence. As a matter of recall, a geometric sequence or geometric progression can be considered as the 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 presented as,

Where,

gn is the nth term that has to be found

g1 is the 1st term in the series

Assume that r is the common ratio.

Solved Example

Problem: Find the 5th term of a geometric sequence where the first term a1=3, and the common ratio r=2

Solution:

Given, 

a1=3

r=2

n=5

Where, 

Therefore, the 5th term=48. 

Uses:

Finance: Compound interest is often represented using geometric sequences to find the value of an investment at a future date.

Population Growth: Biology- Population growth can be rather accurately approximated as a geometric sequence, with multiplication in one generation by a constant factor.

Physics: Geometric sequences directly apply to the type of decay mentioned above, where some quantity decays over time based on some fixed ratio.

Computer Science: Algorithms that contain repeated multiplications or exponential growth often utilize geometric sequences when analyzing the complexity of recursive algorithms.

Real Estate: Normally, property value appreciates according to a geometric sequence, an increase of a fixed percentage every year.

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