# Tips And Tricks And Shortcuts on Geometric Progressions ## Tips,Tricks And Shortcuts To Solve Geometric Progression

GeometricProgression is used in mathematics or aptitude, and they have various applications in physics, engineering, biology, economics, computer science, queueing theory, finance and  geometric. Because in this sequence each successive term can be obtained by multiplying the previous term .

### Tips and Tricks on Geometric Progression easily

• Definition

In the Geometric Progression , the ratio of any term to its preceding term is constant in a sequence of numbers . Geometric Progression is a sequence of numbers where each term is calculated by multiplying the previous one by a fixed, non-zero number called the common ratio

• 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 : 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 = 2

an-1= the term before the nth term,

n = number of terms

In the given series,

r (common ratio) = 4/2 = 2

Therefore, 11th term = a11

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.

Correct option: C

### 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

Correct option: D

### 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)1/3

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

Correct option: C

Read Also  – Formulas To Solve Geometric Progression