## Related Words

# GEOMETRIC SEQUENCE

## Definition of Geometric Sequence

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*term of a geometric sequence is

^{th}*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.]