# Geometric Progressions Questions and Answers

## Geometric progression Questions 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. Application of Geometric Progression is in physics, engineering, biology, economics, computer science, queueing theory, and finance that’s why Geometric Progression Questions and Answers is important to know. Geometric Progression Questions are in the form a, ar, ar², ar³ and so on.
The First term is denoted as = a
The common ratio is denoted as = r 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

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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. 363

363

362

362

242

242

243

243

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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

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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

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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? 3

3

1

1

2

2

8

8

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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

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Question 7 Time: 00:00:00
What is the sum of below given infinite g.p.?

$\frac{1}{2} +\frac{1}{3}+\frac{1}{4} +\frac{1}{9} +\frac{1}{8} +\frac{1}{27}+$…………………..= $\frac{1}{2}$

$\frac{1}{2}$

$\frac{2}{3}$

$\frac{2}{3}$

$\frac{2}{5}$

$\frac{2}{5}$

$\frac{3}{2}$

$\frac{3}{2}$

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Question 8 Time: 00:00:00
How do you find $s_{17}$ 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

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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

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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

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Question 11 Time: 00:00:00
If r = $\frac{1}{2}$ and n=4, then G.P. series will be? $a_{1},\frac{a_{1}}{2},\frac{a_{1}}{4},\frac{a_{1}}{8}$

$a_{1},\frac{a_{1}}{2},\frac{a_{1}}{4},\frac{a_{1}}{8}$

$a_{1},\frac{-a_{1}}{2},\frac{-a_{1}}{4},\frac{-a_{1}}{8}$

$a_{1},\frac{-a_{1}}{2},\frac{-a_{1}}{4},\frac{-a_{1}}{8}$

$a_{1},\frac{a_{1}}{4},\frac{a_{1}}{8},\frac{a_{1}}{16}$

$a_{1},\frac{a_{1}}{4},\frac{a_{1}}{8},\frac{a_{1}}{16}$

none of the above

none of the above

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Question 12 Time: 00:00:00
Find Common Ratio of G.P 3,12,48.... 4

4

12

12

13

13

16

16

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Question 13 Time: 00:00:00
Find out the sum to 7th terms if series is like: 3+1+$\frac{1}{3}$ +…… 2.25

2.25

3

3

3.50

3.50

4.50

4.50

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Question 14 Time: 00:00:00
Find out $a_{3}$ for the geometric series if  $s_{n}$= 349.92, r=2, n=5? 11.28

11.28

45.12

45.12

54.32

54.32

23.46

23.46

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Question 15 Time: 00:00:00
Find $a_{1}$ for the geometric series given $s_{n}$=1364, r=-3, n=5? 22.36

22.36

34.67

34.67

14.56

14.56

25.84

25.84

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Question 16 Time: 00:00:00
Find $s_{n}$ if first term=80, common ratio = $\frac{-1}{2}$ and n=7 ? 55

55

58.54

58.54

53.75

53.75

54.35

54.35

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Question 17 Time: 00:00:00
An interest rate caused an amount to rise. The amount on First day is RS 4 and every additional day it increased two times as much as the earlier day. How much will be amount increase in five days? 31

31

84

84

103

103

120

120