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August 11, 2023
Here, are some easy tips and tricks for you to solve Geometric Progression questions quickly, easily , and efficiently in competitive exams.
Question 1: Find 11th term in the series 2,4,8,16 …
Options:
A. 2042
B. 2200
C. 1024
D. 2048
Solution: We know that,
an = arn-1
where
r(common ratio) = \frac{4}{2} = 2
a1= first term = 2
an-1= the term before the nth term,
n = number of terms
In the given series,
r (common ratio) = \frac{4}{2} = 2
Therefore, 11th term = a11
a11 = 2 x 211-1
a11 = 2 x 210
a11 = 2 x 1024
a11 = 2048
Correct option: D
Question 2 : Find last term in the series if there are 7 term in this series 3,15,75,375 …
A. 46875
B. 44875
C. 42875
D. 40875
r(common ratio) = \frac{15}{3} = 5
a1= first term = 3
r (common ratio) = \frac{15}{3} = 5
Therefore, 7th term = a7
a7 = 3 x 57-1
a7 = 46875
Correct option: A
Question 1. Find the number of terms in the GP 6, 12, 24, 48……1536
A. 6
B. 7
C. 9
D. 8
Solution:
We know that,
a1 = 6,
a2 = 12,
r = \frac{12}{6} = 2,
an = 1536
1536 = 6 x 2n-1 (divide both side by 6)
256 = 2n-1
28 = 2n-1
8 = n – 1
n = 9
Therefore, there are 9 terms in the series.
Correct option: C
Question 2. Find the number of terms in the GP where a1 = 10, a2 = 40 ,a3 = 160 ,an = 10240
A. 10
D. 6
a1 = 10,
a2 = 40,
r = \frac{40}{10} = 4,
an = 10240
10240 = 10 x 4n-1 (divide both side by 10)
1024 = 4n-1
45 = 4n-1
5 = n – 1
n = 6
Therefore, there are 6 terms in the series.
Question 1. How many terms of the series 1 + 3 + 9 +….sum to 121
A. 18
B. 19
C. 13
D. 5
s_{n} = a \times \frac{r^{n} -1}{r-1} if r>1
a = 1,
r = \frac{3}{1} = 3,
Sn = 121
121 =1\times \frac{3^{n} -1}{3-1}
121 = \frac{3^{n} -1}{3-1}
242 = (3n – 1)
243 = 3n
35 = 3n
n = 5
Question 2. Find Sum of given Geometric Series upto 9th term 7,14,28,56……
A. 3177
B. 3577
C. 1377
D. 5377
a = 7,
r = \frac{14}{7} = 2,
Sn = 7\times \frac{2^{9} -1}{2-1}
= 3577
Correct option: B
Question 1. What is the geometric mean of 2, 3, and 6?
Options
A. 4.5
B. 6.5
C. 3.30
D. 6.4
GM = (abc)^{\frac{1}{3}}
Therefore, there Geometric Mean (GM) = (2\times 3\times 6)^{\frac{1}{3}}
= 3.30
Question 2 . What is the geometric mean of 36 and 9?
A. 24
B. 16
C. 18
D. 14
GM = (ab)^{\frac{1}{2}}
Therefore, there Geometric Mean (GM) = (36\times 9)^{\frac{1}{2}}
= 18
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