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

Tips and Tricks for Geometric Progression

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

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

 

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