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.
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
- Read Also – How to solve geometric questions quickly
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