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)