Geometric Progressions Questions and Answers

Geometric Progressions Questions

Formula

Definition of G.P.

A geometric progression is a kind of order that includes an organized and immeasurable assortment of real numbers, wherein every term is acquired by multiplying its previous term through a constant value. Furthermore, the progression of the wat: a, ar, ar², ar³and so on is known as a GP.
The foremost term is denoted as = a
The common ratio is denoted as = r

Formula or Rule for solving G.P.

  • The nth term, Tn = arn– 1
  • Sum to n terms,
    Sn =(a (1-rn))/((1-r)), When r < 1 and Sn =(a (r(n-1)))/((r-1)), When r > 1
  • If x, y, z are in GP, then y is the geometric mean between x and z. In this case,
    y = √xz
  • The sum of an infinite GP a, ar, ar2 and so on is a/(1-r)
  • If ‘a’ is known as the foremost term, and ‘r’ is the common ratio of a limited G.P. which consists of m terms, then from the end the nth term will be = ar(m-n).
  • If the last term is denoted as ‘l’ and common ratio as ‘r’, then from the end the nth of the G.P. will be calculated as: l/(r(n-l)).

Question 1

Time: 00:00:00
How do you find S7 for the geometric series 1 + 9 + 81 + 729 +…?

6,94,765

6,94,765

5,97,871

5,97,871

2,44,406

2,44,406

None of the above

None of the above

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 2

Time: 00:00:00
Find the sum of the geometric series 3 + 9 + 27 + 81 + . . . where there are 5 terms in the series.

243

243

-243

-243

242

242

-242

-242

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 3

Time: 00:00:00
Find the sum of the geometric series 8 − 4 + 2 − 1 + . . where there are 7 terms in the series.

5.37

5.37

5.50

5.50

6.34

6.34

None of the above

None of the above

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 4

Time: 00:00:00
How many terms are there in the geometric progression 4, 8, 16, . . ., 512?

5

5

6

6

7

7

8

8

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 5

Time: 00:00:00
If the common ratio in a specific series is 3. Last term is 486 and sum of the terms is 728. Then find out the first term of gp?

1

1

2

2

8

8

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 6

Time: 00:00:00
How do you find S₁₀ for the geometric series 1 + 5 + 25 + 125 +…?

25,00,000

25,00,000

23,87,463

23,87,463

24,41,406

24,41,406

None of the above

None of the above

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 7

Time: 00:00:00
What is the sum of below given infinite g.p.?

½+1/3+1/4+1/9+1/8+1/27+…………………..=

½

½

2/3

2/3

2/5

2/5

3/2

3/2

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 8

Time: 00:00:00
How do you find S₁₇ for the geometric series 5 + 15 + 45 + 135 + …?

32,28,50,405

32,28,50,405

12,91,40,631

12,91,40,631

34,2154,214

34,2154,214

None of the above

None of the above

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 9

Time: 00:00:00
How do you find the sum of the first 6 terms of the geometric series: 6+ 36 + 216…?

33454

33454

55986

55986

43659

43659

76463

76463

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 10

Time: 00:00:00
Find out the sum of the next infinite geometric series, if it exists? 3 + 2.25 + 1.6875 + 1.265625+…?

10

10

11

11

12

12

13

13

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 11

Time: 00:00:00
If r=1/2 and n=4, then G.P. series will be?

a₁,a₁/2,a₁/4,a₁/8

a₁,a₁/2,a₁/4,a₁/8

a₁,-a₁/2,-a₁/4,-a₁/8

a₁,-a₁/2,-a₁/4,-a₁/8

a₁,a₁/4,a₁/8,a₁/16

a₁,a₁/4,a₁/8,a₁/16

none of the above

none of the above

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 12

Time: 00:00:00
What is the sum of the geometric series Σ6 (2)n from n=1 to 8?

1022

1022

1023

1023

6132

6132

5556

5556

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 13

Time: 00:00:00
Find out the sum to 7th terms if series is like:3+1+1/3 +……

2.25

2.25

3

3

3.50

3.50

4.50

4.50

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 14

Time: 00:00:00
Find out a₃ for the geometric series if Sn=349.92, r=2, n=5?

11.28

11.28

45.12

45.12

54.32

54.32

23.46

23.46

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 15

Time: 00:00:00
Find a1 for the geometric series given Sn=−1364, r=-3, n=5?

22.45

22.45

34.67

34.67

14.56

14.56

25.84

25.84

Once you attempt the question then PrepInsta explanation will be displayed.

Please login to submit your explanation

Start

Question 16