Nth Term of Geometric Progression

The terms of a GP are represented as a1, a2, a3, a4, …, an.

Expressing all these terms according to the first term a1, we get

a1 = a
a2 = a1r
a3 = a2r = (a1r)r = a1r2
a4 = a3r = (a1r2)r = a1r3

am = a1rm−1

Similarly,
an = a1rn – 1

General term or nth term of a Geometric Sequence a, ar, ar2, ar3, ar4 is given by : 

an = arn-1

where, 

a1 = first term, 
a2 = second term
an = last term (or the nth term)

Nth Term from the Last Term is given by:

an = l/rn-1

where,
l is the last term

Geometric Progression (GP) | Formula and Properties

Geometric Progression (GP): In Maths, A Geometric Progression (GP) is a type of sequence where each succeeding term is obtained by multiplying each preceding term by a fixed number which is called the common ratio (r). This progression is also known as a geometric sequence of numbers that follow a pattern.

In this article, we will cover Geometric Progression (GP), its formula, the general form of GP, its properties, types, sum of n terms of GP, Arithmetic progression vs geometric progression, etc.

Table of Content

  • What is Geometric Progression (GP)?
    • Geometric Progression Definition
  • Geometric Progression Formula
  • General Form of Geometric Progression
  • Nth Term of Geometric Progression
  • Sum of N Terms of GP
    • Sum of Infinite Geometric Progression
  • Properties of Geometric Progression
  • Types of Geometric Progression
    • Finite Geometric Progression
    • Infinite Geometric Progression
  • Geometric Sequence Recursive Formula
  • Geometric Progression vs Arithmetic Progression
  • Solved Examples on Geometric Progression (GP)

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