Tips And Tricks And Shortcuts on Geometric Progressions

November 14, 2019

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

Options:

A. 2042

B. 2200

C. 1024

D. 2048

Solution:

We know that,

a_n = ar^n-1

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

, a₁= first term, a_n-1= the term before the n^th term, n = number of terms

In the given series,

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

Therefore, 11^th term = a₁₁ = an = ar^n-1

a₁₁ = 2 * 2^11-1

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,

a_n= 1536

an = ar^n-1

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

256 = 2^n-1

2⁸ = 2^n-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,

S_n = {a₁[(rⁿ)-1]}/(r-1) , (r>1)

In the given series,

a = 1, r =3/1 = 3, S_n = 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

Read Also – How to solve geometric questions quickly

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