A geometric progression is a type of sequence characterized by an ordered and infinite collection of real numbers, where each term is obtained by multiplying its preceding term by a constant value.
a, ar, ar^{2}, ar^{3}, ……..
where,
The first term is denoted as = a
The common ratio is denoted as = r
Geometric progression can be classified based on the number of terms in the sequence.
Geometric Progression finds application in physics, engineering, biology, economics, computer science, queueing theory, and finance. This underscores the importance of understanding Geometric Progression questions and answers.
Example 1: How do you find S_{7} for the geometric series 1 + 9 + 81 + 729 +…?
(a) 6,94,765
(b) 5,97,871
(c) 2,44,406
(d) None of the above
Ans: (b)
First term a = 1 and r = 9.
= 5,97,871
Example 2: Find the sum of the geometric series 8, − 4, + 2, − 1,. . . where there are 7 terms in the series.
(a) 5.37
(b) 5.50
(c) 6.34
(d) None of the above
Ans: (a)
For this series, we have a = 8, r = 1/2 and n = 7
Thus
S_{7} =5.37.
Example 3: If Product of 3 successive terms of Geometric Progression is 8 then mid of those 3 successive terms will be
(a) 2
(b) 12
(c) 4
(d)13
Ans: (a)
Let x/r , x, xr be three terms ,then
x = 2
Example 4: What is the sum of below given infinite g.p.?
(a) 1/2
(b) 2/3
(c) 2/5
(d) 3/2
Ans: (d)
Example 5: How do you find the sum of the first 6 terms of the geometric series: 6+ 36 + 216…?
(a) 33454
(b) 55986
(c) 43659
(d) 76463
Ans: (b)
Common ratio = 6 and First term = 6
As per the formula:
= 55986
Example 6: Find the sum of the geometric series 3 + 9 + 27 + 81 + . . . where there are 5 terms in the series.
(a) 363
(b) 362
(c) 242
(d) 243
Ans: (a)
For this series, we have a = 3, r = 3 and n = 5.
Example 7: How many terms are there in the geometric progression 4, 8, 16, . . ., 512?
(a) 5
(b) 6
(c) 7
(d) 8
Ans: (d)
Here a = 4 and r = 2. nth term = 512. But the formula for the nth term is ar^{n−1}
So
512 = 4 × 2^{n−1 }
128 = 2^{n−1}
2^{7 }= 2^{n−1}
7 = n − 1
n = 8.
Example 8: How do you find S₁₀ for the geometric series 1 + 5 + 25 + 125 +…?
(a) 25,00,000
(b) 23,87,463
(c) 24,41,406
(d) None of the above
Ans: (c)
As we know first term a=1 and r=5.
= 24,41,406
Example 9: How do you find s_{17} for the geometric series 5 + 15 + 45 + 135 + …?
(a) 32,28,50,405
(b) 12,91,40,631
(c) 34,2154,214
(d) None of the above
Ans: (a)
As we know first term a=5 and r=3.
=32,28,50,405
Example 10: Find out the sum of the next infinite geometric series, if it exists? 3 + 2.25 + 1.6875 + 1.265625+…?
(a) 10
(b) 11
(c) 12
(d) 13
Ans: (c)
Here a = 3
r = 0.75
Since r<1
314 videos170 docs185 tests

1. What is a geometric progression? 
2. How is a geometric progression different from an arithmetic progression? 
3. Can a geometric progression have a negative common ratio? 
4. What is the formula to find the nth term of a geometric progression? 
5. How can geometric progressions be applied in reallife situations? 
314 videos170 docs185 tests


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