Geometric Progression MCQ Quiz - Objective Question with Answer for Geometric Progression - Download Free PDF
Last updated on Jun 15, 2025
Latest Geometric Progression MCQ Objective Questions
Geometric Progression Question 1:
If the first term is 27 and the common ratio is 2/3, what will be the 4th term of the GP?
Answer (Detailed Solution Below)
Geometric Progression Question 1 Detailed Solution
Given:
First term (a) = 27
Common ratio (r) = 2/3
Find the 4th term of the GP.
Formula used:
n-th term of GP = a × r(n-1)
Calculation:
4th term = 27 × (2/3)(4-1)
⇒ 4th term = 27 × (2/3)3
⇒ 4th term = 27 × (8/27)
⇒ 4th term = 8
∴ The correct answer is option (1).
Geometric Progression Question 2:
The 4th term of a G.P. is square of its second term and the first term is -3, then the 7th term of the G.P is
Answer (Detailed Solution Below)
Geometric Progression Question 2 Detailed Solution
Concept:
Let us consider sequence a1, a2, a3 …. an is a G.P.
- Common ratio = r =
- nth term of the G.P. is an = arn−1
- Sum of n terms of GP = sn =
; where r >1 - Sum of n terms of GP = sn =
; where r - Sum of infinite GP =
; |r|
Calculation:
Given: 4th term of a G.P. is square of its second term
So, ar3 = (ar)2
⇒ ar3 = a2r2
⇒ r = a .... (i)
Also given, the first term is -3
So, a = -3
Put the value of 'a' in equation (i), we get
r = a = -3
Now, 7th term of the G.P = ar6
= -3 × (-3)6
= -2187
Geometric Progression Question 3:
If m, n, o are in geometric progression, then which is true among the following?
Answer (Detailed Solution Below)
Geometric Progression Question 3 Detailed Solution
Concept:
In a geometric progression, the ratio between 2 consecutive terms remains constant.
Calculation:
Considering G.P of m, n, o let the common ratio be k1.
∴
Thus it is a geometric progression
Top Geometric Progression MCQ Objective Questions
If m, n, o are in geometric progression, then which is true among the following?
Answer (Detailed Solution Below)
Geometric Progression Question 4 Detailed Solution
Download Solution PDFConcept:
In a geometric progression, the ratio between 2 consecutive terms remains constant.
Calculation:
Considering G.P of m, n, o let the common ratio be k1.
∴
Thus it is a geometric progression
If the first term is 27 and the common ratio is 2/3, what will be the 4th term of the GP?
Answer (Detailed Solution Below)
Geometric Progression Question 5 Detailed Solution
Download Solution PDFGiven:
First term (a) = 27
Common ratio (r) = 2/3
Find the 4th term of the GP.
Formula used:
n-th term of GP = a × r(n-1)
Calculation:
4th term = 27 × (2/3)(4-1)
⇒ 4th term = 27 × (2/3)3
⇒ 4th term = 27 × (8/27)
⇒ 4th term = 8
∴ The correct answer is option (1).
Geometric Progression Question 6:
The 4th term of a G.P. is square of its second term and the first term is -3, then the 7th term of the G.P is
Answer (Detailed Solution Below)
Geometric Progression Question 6 Detailed Solution
Concept:
Let us consider sequence a1, a2, a3 …. an is a G.P.
- Common ratio = r =
- nth term of the G.P. is an = arn−1
- Sum of n terms of GP = sn =
; where r >1 - Sum of n terms of GP = sn =
; where r - Sum of infinite GP =
; |r|
Calculation:
Given: 4th term of a G.P. is square of its second term
So, ar3 = (ar)2
⇒ ar3 = a2r2
⇒ r = a .... (i)
Also given, the first term is -3
So, a = -3
Put the value of 'a' in equation (i), we get
r = a = -3
Now, 7th term of the G.P = ar6
= -3 × (-3)6
= -2187
Geometric Progression Question 7:
If m, n, o are in geometric progression, then which is true among the following?
Answer (Detailed Solution Below)
Geometric Progression Question 7 Detailed Solution
Concept:
In a geometric progression, the ratio between 2 consecutive terms remains constant.
Calculation:
Considering G.P of m, n, o let the common ratio be k1.
∴
Thus it is a geometric progression
Geometric Progression Question 8:
If the first term is 27 and the common ratio is 2/3, what will be the 4th term of the GP?
Answer (Detailed Solution Below)
Geometric Progression Question 8 Detailed Solution
Given:
First term (a) = 27
Common ratio (r) = 2/3
Find the 4th term of the GP.
Formula used:
n-th term of GP = a × r(n-1)
Calculation:
4th term = 27 × (2/3)(4-1)
⇒ 4th term = 27 × (2/3)3
⇒ 4th term = 27 × (8/27)
⇒ 4th term = 8
∴ The correct answer is option (1).