Geometric Progression(GP)

Definition:
A progression of numbers in which every term bears a constant ratio with the preceeding term is called Geometric progression.
The constant ratio is called the common ratio of the GP
If the first term is a and common ratio is r then,
GP is a,ar,ar²,ar³,…..

Formula:
Tn = ar^n-1
Sn = (a(1-rⁿ))/(1-r)
Where,
Tn is the nth term in the GP,
Sn is the sum of n terms in the GP,
a is the first term,
r is the common ratio of the GP,
n is the number of term in the GP.

Example1:
Find the 10 th term in the GP 2,4,8,16,….
Solution:

	Step1:
		Use the formula, Tn = arn-1
	Step2:
		In the given problem,
		a=first term=2
		r=common ratio=2
		(to find common ratio take any two terms in the GP and find the quotient(4/2=2))
		n=10
	Step3:
		Apply values of step 2 in step 1
		T10=2 * 2 9
		=1024
		The 10 th term in the given GP is 1024

Example2:
Find the sum of 5 terms in the GP 2,4,8,16,….
Solution:

	Step1:
		Use the formula, Sn = (a(1-rn))/(1-r)
	Step2:
		In the given problem,
		a=first term=2
		r=common ratio=2
		(to find common ratio take any two terms in the GP and find the quotient(4/2=2))
		n=5
	Step3:
		Apply values of step 2 in step 1
		S5=(2 * (1-25))/(1-2)
		=62
		The sum of 5 terms in the given GP is 62

Geometric progression(GP)

is explained in this article
For details regarding Arithmetic Progression click here