Geometric sequence is a sequence in which each term after the first term a is obtained by multiplying the previous term by a constant r, called the common ratio. It is obvious that a ≠ 0 and r ≠ 0 or 1

Example: 1, 2, 4, 8, 16, 32, . . . is a geometric sequence
Each term of this geometric sequence is multiplied by the common ratio 2

More About Geometric Sequence

The general form of a geometric sequence with first term a and common ratio r is a, ar, ar^{2}, ar^{3} ................. ar^{(n-1)}
The general term or n^{th} term of a geometric sequence is ar^{(n-1)}
Geometric series is the indicated sum of the terms of a geometric sequence.
For the geometric sequence 1, 2, 4, 8, 16, 32, the corresponding geometric series is1 + 2 + 4 + 8 + 16 + 32

Video Examples: Geometric Sequences (Introduction)

Solved Examples on Geometric Sequence

Ques: Which of the following is a geometric sequence?

Choices:

A. 2, 4, 8, 16, 30, 32,......
B. 2, 4, 6, 8, 16, 32, 64,....
C. 2, 4, 8, 12, 18, 24,......
D. 2, 4, 8, 18, 36, 64,.....

Correct Answer: B

Solution:

Step1: Geometric sequence is a sequence in which each term after the first term is obtained by multiplying the previous term by a constant
Step 2: 2, 4, 6, 8, 16, 32, 64,...... is the only sequence in the options in which each term is obtained by multiplying the previous term by 2

Ques: Find the 5th term of the geometric sequence 1/3,1,3.......

Choices:

A. 9
B. 3
C. 81
D. 27

Correct Answer: D

Solution:

Step 1: In a geometric sequence, the nth term is given by an = a1 rn - 1
Step 2: To find the fifth term, substitute n = 5, a_{1} = 1/3 and r = 3 in the formula
Step 3: The 5th term is [Substitute and simplify.]