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SSC CGL Exam  >  SSC CGL Test  >  Quantitative Aptitude  >  MCQ: Geometric Progressions - 1 - SSC CGL MCQ

Geometric Progressions - 1 - Free MCQ Practice Test with solutions, SSC


MCQ Practice Test & Solutions: MCQ: Geometric Progressions - 1 (15 Questions)

You can prepare effectively for SSC CGL Quantitative Aptitude for SSC CGL with this dedicated MCQ Practice Test (available with solutions) on the important topic of "MCQ: Geometric Progressions - 1". These 15 questions have been designed by the experts with the latest curriculum of SSC CGL 2026, to help you master the concept.

Test Highlights:

  • - Format: Multiple Choice Questions (MCQ)
  • - Duration: 15 minutes
  • - Number of Questions: 15

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MCQ: Geometric Progressions - 1 - Question 1
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A sequence is called ___________________ if an+1 = an * r.

Detailed Solution: Question 1

Clarification: A sequence is called geometric progression if an+1 = an * r where a1 is the first term and r is common ratio.

MCQ: Geometric Progressions - 1 - Question 2
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If first term of a G.P. is 20 and common ratio is 4. Find the 5th term.

Detailed Solution: Question 2

Given, a = 20 and r = 4.
We know, an = arn-1
⇒ a5 = 20*44 = 20*256 = 5120.

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MCQ: Geometric Progressions - 1 - Question 3
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If r = 1 in a G.P. then what is the sum to n terms?

Detailed Solution: Question 3

If a is the first term of G.P., then G.P. look like a, a, a, a, …………
Then sum to n terms becomes n*a.

MCQ: Geometric Progressions - 1 - Question 4
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In G.P. 4, 8, 16, 32, ………… find the sum up to 5th term.

Detailed Solution: Question 4

In the given G.P., a = 4 and r = 8/4 = 2.
We know, Sn = a(rn-1)/(r-1)
⇒ S5 = 4(25-1) / (2-1) = 4*31 = 124.

MCQ: Geometric Progressions - 1 - Question 5
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In a G.P., 5th term is 27 and 8th term is 729. Find its 11th term.

Detailed Solution: Question 5

Given, a5 = 27 and a8 = 729.
⇒ ar4 = 27 and ar7 = 729
On dividing we get, r3 = 27 ⇒ r = 3
⇒ a = 27 / (34) = 1/3
⇒ a11 = ar10 = (1/3) (310) = 39 = 19683.

MCQ: Geometric Progressions - 1 - Question 6
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How many terms of G.P. 2,4,8,16, …………… are required to give sum 254?

Detailed Solution: Question 6

a=2 and r = 4/2 = 2.
We know, Sn = a(rn-1)/(r-1)
2(2n-1) / (2-1) = 254
=>2n-1 = 127 => 2n = 128 = 27
=> n=7. 

MCQ: Geometric Progressions - 1 - Question 7
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If three positive numbers are inserted between 4 and 512 such that the resulting sequence is a G.P., which of the following is not among the numbers inserted?

Detailed Solution: Question 7

 Let G.P. be 4, G1, G2, G3, 512.
=> a=4 and a5 = a*r4 = 512 => 4*r4 = 512 => r4 = 512/4 = 128 => r = 4.
G1 = a2 = a * r = 4*4 = 16.
G2 = G1 * r = 16 * 4 = 64.
G3 = G2 * r = 64*4 = 256.
Thus, the inserted numbers are 16, 64, and 256. The number not inserted is 128.

MCQ: Geometric Progressions - 1 - Question 8
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The sum of first three terms of a G.P. is 21/2 and their product is 27. Which of the following is not a term of the G.P. if the numbers are positive?

Detailed Solution: Question 8

Let three terms be a/r, a, a*r.
Product = 27 => (a/r) (a) (a*r) = 27 => a3 = 27
=>a = 3.
Sum = 21/2 => (a / r + a + a*r) = 21/2 => a (1 / r + 1 + 1*r) = 21/2
=> (1 / r + 1 + 1*r) = (21/2)/3 = 7/2
=> (r2 + r + 1) = (7/2) r => r2 – (5/2) r +1 = 0
=> r = 2 and 1/2.
Terms are 3/2, 3, 3*2 i.e. 3/2, 3, 6. 

MCQ: Geometric Progressions - 1 - Question 9
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If a sequence is in the form 2*5n then which of the following may be the sequence?

Detailed Solution: Question 9

If an = 2*5n then
a1 =10, a2 = 50, a3=250.
This is a geometric progression with first term 10 and common ratio 5.

MCQ: Geometric Progressions - 1 - Question 10
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If a = 3 and r = 2 then find the sum up 5th term.

Detailed Solution: Question 10

We know, Sn = a(rn-1)/(r-1)
Here a = 3, r = 2 and n = 5
S5 = 3 (25-1) / (2-1) = 3(32 -1) = 3*31 = 93.

MCQ: Geometric Progressions - 1 - Question 11
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Which term of G.P. 25, 125, 625, …………. is 390625?

Detailed Solution: Question 11

In the given G.P., a = 25 and r = 125/25 = 5.
Given, an = 390625 => arn-1 = 390625
=> 25*5n-1 = 390625
=> 5n-1 = 390625/25 = 15625 = 56
=> n-1 = 6 => n=7.

MCQ: Geometric Progressions - 1 - Question 12
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What is nth term of a G.P.?

Detailed Solution: Question 12

Since every term of an G.P. is r times the previous term.
i.e. an+1 = an * r = an-1 * r2 = ….. = a1 * rn
or an = a*rn-1

MCQ: Geometric Progressions - 1 - Question 13
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Find the sum of series 1+1/2 + 1/4 + ………. up to 6 terms.

Detailed Solution: Question 13

Given series is G.P. with first term 1 and common ratio 1/2.
We know, Sn = a(1-rn)/(1-r) for r<1.
S6 = 1(1-(1/2)6) / (1-1/2) = (1-1/64) / (1/2) = 63*2/64 = 63/32. 

MCQ: Geometric Progressions - 1 - Question 14
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The sum of first three terms of a G.P. is 21/2 and their product is 27. Find the common ratio.

Detailed Solution: Question 14

Let three terms be a/r, a, a*r.
Product = 27 => (a/r) (a) (a*r) = 27 => a3 = 27
=>a = 3.
Sum = 21/2 => (a / r + a + a*r) = 21/2 => a (1 / r + 1 + 1*r) = 21/2
=> (1 / r + 1 + 1*r) = (21/2)/3 = 7/2
=> (r2 + r + 1) = (7/2) r => r2 – (5/2) r + 1 = 0
=> r = 2 and 1/2. 

MCQ: Geometric Progressions - 1 - Question 15
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Which of the following is the geometric mean of 3 and 12.

Detailed Solution: Question 15

We know, geometric mean of two numbers a and b is given by

So, G.M. of 3 and 12 is

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This test contains 15 MCQs on MCQ: Geometric Progressions - 1 with detailed solutions for each question. It is part of the Quantitative Aptitude for SSC CGL course on EduRev, designed to align with the current SSC CGL syllabus. Each solution explains not just the correct answer but also gives you an understanding of the topic — not just to attempt the question but also help you prepare for the exam with practice.

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