# Tips And Tricks And Shortcuts on Geometric Progressions

## Tips and Tricks on Geometric Progression easily

Here, are easy tips and tricks for you on Geometric Progression problems easily, and efficiently in competitive exams.

There are 4 types of questions asked in exams

## Type 1: Find nth term of the series

### Question 1.

Find 11th term in the series 2, 4, 6, 8, …

Options:

A. 2042

B. 2200

C. 1024

D. 2048

#### Solution:

We know that,

an = arn-1

where, r(common ratio) = 4/2 = 2

, a1= first term, an-1= the term before the nth term, n = number of terms

In the given series,

a (first term) = 2
r (common ratio) = 4/2 = 2

Therefore, 11th term = a11 = an = arn-1

a11 = 2 * 211-1

a11 = 2 * 210

a11 = 2 * 1024

a11 = 2048

#### Correct option: D ## Type 2: Find number of terms in the series

### Question 1.

Find the number of terms in the GP 6, 12, 24, 48……1536?

Options:

A. 6

B. 7

C. 9

D. 8

#### Solution:

We know that,

In the given series,

a1 = 6, a2 = 12, r =12/6  = 2,

an = 1536

an = arn-1

1536 = 6*2n-1 (divide both side by 6)

256 = 2n-1

28 = 2n-1

8 = n – 1

n = 9

Therefore, there are 9 terms in the series.

## Type 3: Find sum of first ‘n’ terms of the series

### Question 1.

How many terms of the series 1 + 3 + 9 +….sum to 121

Options:

A. 18

B. 19

C. 13

D. 5

#### Solution:

We know that,

Sn = {a1[(rn)-1]}/(r-1) , (r>1)

In the given series,

a = 1, r =3/1  = 3, Sn = 121

121 ={1*[(3n)-1]}/3-1

121 = [(3n)-1]/2

242 = (3n – 1)

243 = 3n

35 = 3n

n = 5

## Type 4: Find the Geometric Mean (GM) of the series.

### Question 1.

What is the geometric mean of 2, 3, and 6?

Options

A. 4.5

B. 6.5

C. 3.30

D. 6.4

#### Solution:

We know that,

GM = √abc

Therefore, there Geometric Mean (GM) = (2*3*6)1/3

This can be written as (2*3*6)1/3

(36) 1/3 = 3.30