# Geometric Progressions Questions ## 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

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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. 243

243

-243

-243

242

242

-242

-242

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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? 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.?

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

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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

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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=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

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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

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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

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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

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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

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