MCQ: Geometric Progressions - 3 - SSC CGL MCQ

# MCQ: Geometric Progressions - 3 - SSC CGL MCQ

Test Description

## 15 Questions MCQ Test Quantitative Aptitude for SSC CGL - MCQ: Geometric Progressions - 3

MCQ: Geometric Progressions - 3 for SSC CGL 2024 is part of Quantitative Aptitude for SSC CGL preparation. The MCQ: Geometric Progressions - 3 questions and answers have been prepared according to the SSC CGL exam syllabus.The MCQ: Geometric Progressions - 3 MCQs are made for SSC CGL 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for MCQ: Geometric Progressions - 3 below.
Solutions of MCQ: Geometric Progressions - 3 questions in English are available as part of our Quantitative Aptitude for SSC CGL for SSC CGL & MCQ: Geometric Progressions - 3 solutions in Hindi for Quantitative Aptitude for SSC CGL course. Download more important topics, notes, lectures and mock test series for SSC CGL Exam by signing up for free. Attempt MCQ: Geometric Progressions - 3 | 15 questions in 15 minutes | Mock test for SSC CGL preparation | Free important questions MCQ to study Quantitative Aptitude for SSC CGL for SSC CGL Exam | Download free PDF with solutions
MCQ: Geometric Progressions - 3 - Question 1

### If the 4th, 7th and 10th terms of a G.P. be a, b, c respectively, then the relation between a, b, c is

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 1

Concept:
Geometric Progression
The general form of Geometric Progression is:
a, ar, ar2, ar3, ar4,…, arn-1
where, a = First term, r = common ratio, arn-1 = nth term.

Calculation:
Let A be first term of GP with common ratio r.
The nth term, An = Arn-1
Given 4th term = a
Ar3 = a …(i)
Given 7th term = b
Ar6 = b …(ii)
Given 10th term = c
Ar9 = c …(iii)
Multiply (i) and (iii)
⇒ ac = Ar3(Ar9)
⇒ ac = A2r12
⇒ ac = (Ar6)2
⇒ ac = b2
∴ b2 = ac

MCQ: Geometric Progressions - 3 - Question 2

### If  21/e, 2b/ac, 21/a are in GP, then which one of the following is correct ?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 2

Concept:
If three terms p, q, r are in GP, then pr = q2.
If three terms a, b, c are in AP, then 2b = a + c

Calculation:

⇒ a, b, c are in AP
∴ The correct option is (1).

 1 Crore+ students have signed up on EduRev. Have you?
MCQ: Geometric Progressions - 3 - Question 3

### In a G.P , the 5th term is 96 and 8th term is 768 , then the 3rd term of G.P is  ?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 3

Concept :

Let us consider sequence a1, a2, a3 …. an is a G.P.

• Common ratio ,
• nth term of G.P  is  an = arn-1
• Sum of n terms =
• Sum of n terms =
• Sum of infinite

Calculation:
Here 5th term of G.P is 96
i.e  a5 = ar5-1
⇒ a5 = ar4
⇒ 96 = ar4        ____( i )
Given: 8th term is 768
⇒ a8 = ar7
768 = ar7       ____(ii)
Divide eqn. (ii) by eqn. (i) , we get
8 = r
⇒ r = 2.
Putting this in eqn. (i) , we get
a = 6.
We know that , nth term of G.P , an = arn-1
So, a3 = 6× 23-1
⇒ a3 = 24 .
The correct option is 3.

MCQ: Geometric Progressions - 3 - Question 4

If the sum of n numbers in the GP 5, 10, 20, ... is 1275 then n is ?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 4

Concept:
Let us consider sequence a1, a2, a3 …. an is a G.P.

• Common ratio =
• nth  term of the G.P. is an = arn−1
• Sum of n terms of GP =
• Sum of n terms of GP =
• Sum of infinite GP =

Calculation:
Given series is 5, 10, 20, ...
Here, a = 5, r = 2
Sum of n numbers = sn = 1275
To Find: nAs we know that, Sum of n terms of GP where r >1

1275 = 5 × (2n - 1)
⇒ 255 = (2n - 1)
⇒ 2n = 256
⇒ 2n = 28
∴ n = 8

MCQ: Geometric Progressions - 3 - Question 5

In a G.P.  of positive terms , if every term is equal to the sum of next two terms. Then find the common ratio of the G.P.

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 5

Concept:
Let us consider sequence a1, a2, a3 …. an is a G.P.

• Common ratio =
• nth  term of the G.P. is an = arn−1

Sin18o

Calculation:
We know that if the first term of a G.P is 'a' and the common ratio is 'r' then in this case then G.P = a, ar, ar2............
Since we have given  a = ar + ar
Now, 1= r + r2
⇒ r2 + r - 1 = 0
After solving we get

MCQ: Geometric Progressions - 3 - Question 6

The value of  is:

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 6

Concept:
Geometric Progression (GP):

• The series of numbers where the ratio of any two consecutive terms is the same is called a Geometric Progression.
• A Geometric Progression of n terms with first term a and common ratio r is represented as:
a, ar, ar2, ar3, ..., arn-2, arn-1.
• The sum of the first n terms of a GP is:
• The sum to ∞ of a GP, when |r| < 1, is:

Calculation:

Let us consider the infinite series

MCQ: Geometric Progressions - 3 - Question 7

The third term of a GP is 3. What is the product of its first five terms?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 7

Concept:

Let us consider sequence a1, a2, a3 …. an is a G.P.
Common ratio

Calculation:
Consider,
(a = 3) be the 3rd term of the G.P series,
So, we can write the five terms as,

So, the product of the five terms (P) will be,

Since,
a = 3,
∴ The product of the first five terms (P) = 35 = 243

MCQ: Geometric Progressions - 3 - Question 8

What is the nth term of the sequence 25, -125, 625, -3125, …….?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 8

Concept:
If a1, a2, …., an is a GP then the general term is given by: an = a × rn - 1 where a is the 1st term and r is the common ratio.

Calculation:
Given: 25, -125, 625, -3125, …….
Here, first term a = 25 and common ratio r = -5.
As we know that, if a1, a2, …., an is a GP then the general term is given by: an = a × rn - 1 where a is the first term and r is the common ratio.
⇒ The general term is : an = 25 × (-5)n – 1 = (-1)n – 1 × 5n + 1

MCQ: Geometric Progressions - 3 - Question 9

The terms of a G.P. are positive. If each term is equal to the sum of two terms that follows it, then the common ratio is

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 9

Concept:
The general form of Geometric Progression is:
a, ar, ar2, ar3, ar4,…, arn-1
Where,
a = First term
r = common ratio
arn-1 = nth term

Calculation:
It is given that each term is equal to the sum of two terms that follows it.
Tn = Tn+1 + Tn+2
⇒ arn-1 = arn + arn+1
⇒ rn-1 = rn + rn+1
⇒ r-1 = r + 1
⇒ r2 + r - 1 = 0

Since each term of the G.P. is positive,

∴ The common ratio is

MCQ: Geometric Progressions - 3 - Question 10

If nth term of a G.P. is 2n then find the sum of its first 6 terms.

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 10

Concept:
Sum of n terms of a Geometric Progression,

Given that an = 2n of the G.P.
Then, a1 = 2
a2 = 4
a3 = 8
i.e. G.P. series is 2, 4, 8, 16, 32, . . .
where first term, a = 2 ;
Common ration, r = 4/2 = 8/ 4 = ... = 2,
Number of terms, n = 6 (given in the question)

⇒ 2(64 - 1)
⇒ 2(63)
⇒ 126

MCQ: Geometric Progressions - 3 - Question 11

The third term of a G.P. is 9. The product of its first five terms is

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 11

Concept:
Five terms in a geometric progression:
If a G.P. has first term a and common ratio r then the five consecutive terms in the GP are of the form

Calculation:
Let us consider a general geometric progression with common ratio r.
Assume that the five terms in the GP are

It is given that third term is 9.
Therefore, a = 9.
Now the product of the five terms is given as follows:

But we know that a = 9.
Thus, the product is 95 = 310.

MCQ: Geometric Progressions - 3 - Question 12

For what possible value of x are the numbers - 2/7, x, - 7/2 are in a GP ?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 12

Concept:
If a, b and c are in a GP then b2 = ac

Calculation:
Given: The numbers - 2/7, x, - 7/2 are in GP
As we know that, if a, b and c are in GP then b2 = ac
Here, a = - 2/7, b = x and c = - 7/2
⇒ x2 = (-2/7) × (-7/2) = 1
⇒ x = ± 1
Hence, correct option is 3.

MCQ: Geometric Progressions - 3 - Question 13

A man has 2 parents, 4 grandparents, 8 great- grand parents, and so on . Find the number of ancestors during the 8 generations preceding his own .

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 13

Concept:

Let us consider sequence a1, a2, a3 …. an is an G.P.

• Sum of n terms =
• Sum of n terms =

Calculation:
The required no. of ancestors
= 2 + 4 + 8 +... upto 8 terms
As we know that sum  of G.P ,

Where , a = 2, r = 2 and n = 8
⇒ No. of ancestors required
∴ No. of ancestors required is  510.
The correct option is 4.

MCQ: Geometric Progressions - 3 - Question 14

For the series 1 + 3 + 32 + ... , the sum to n terms is 3280. Find the value of n.

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 14

Concept:
Geometric Progression (GP):
The series of numbers where the ratio of any two consecutive terms is the same, is called a Geometric Progression.

• A Geometric Progression of n terms with first term a and common ratio r is represented as:
• a, ar, ar2, ar3, ..., arn-2, arn-1.
• The sum of the first n terms of a GP is

Calculation:
For the given geometric series 1 + 3 + 32 + ..., we have a = 1 and r = 3.
Let the sum of first n terms be equal to 3280.

⇒ 3n - 1 = 3280 × 2
⇒ 3n - 1 = 6560
⇒ 3n = 6561 = 38
⇒ n = 8.

MCQ: Geometric Progressions - 3 - Question 15

If the sum of n numbers in the GP 4, 8, 16, ... is 2044 then n is ?

Detailed Solution for MCQ: Geometric Progressions - 3 - Question 15

Concept:

Let us consider sequence a1, a2, a3 …. an is a G.P.

• Common ratio =
• nth  term of the G.P. is an = arn−1
• Sum of n terms of GP =
• Sum of n terms of GP =
• Sum of infinite GP =

Calculation:
Given series is 4, 8, 16, ...
Here, a = 4, r = 2
Sum of n numbers = sn = 2044
To Find: nAs we know that, Sum of n terms of GP

2044 = 4 × (2n - 1)
⇒ 511 = (2n - 1)
⇒ 2n = 512
⇒ 2n = 29
∴ n = 9

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests
Information about MCQ: Geometric Progressions - 3 Page
In this test you can find the Exam questions for MCQ: Geometric Progressions - 3 solved & explained in the simplest way possible. Besides giving Questions and answers for MCQ: Geometric Progressions - 3, EduRev gives you an ample number of Online tests for practice

## Quantitative Aptitude for SSC CGL

314 videos|170 docs|185 tests