In a geometric progression (GP), each successive term is obtained by multiplying a constant number with its preceding term. If we divide any succeeding term by its preceding term, we obtain a value equal to the common ratio.
Example 1: Find 11^{th} term in the series 2,4,8,16 …
(a) 2042
(b) 2200
(c) 1024
(d) 2048
Ans: (d)
We know that,
a_{n} = ar^{n1}
where
r(common ratio) = 4/2 = 2
a_{1}= first term = 2
a_{n1 }= the term before the n^{th} term,
n = number of terms
In the given series,
r (common ratio) = 4/2 = 2
Therefore, 11^{th} term = a_{11}
a_{11} = 2 x 2^{111}
a_{11} = 2 x 2^{10}
a_{11} = 2 x 1024
a_{11 }= 2048
Example 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
Ans: (a)
We know that,
a_{n} = ar^{n1}
where
r(common ratio) = 15/3 = 5
a_{1}= first term = 3
a_{n1}= the term before the n^{th} term,
n = number of terms
In the given series,
r (common ratio) = 15/3 = 5
Therefore, 7^{th} term = a_{7}
a_{7} = 3 x 5^{71}
a_{7 }= 46875
We know that,
In the given series,
a_{1 }= 10,
a_{2} = 40,
r = 40/10 = 4
a_{n }= 10240
a_{n} = ar^{n1}
10240 = 10 x 4^{n1} (divide both side by 10)
1024 = 4^{n1}
4^{5} = 4^{n1}
5 = n – 1
n = 6
Therefore, there are 6 terms in the series.
Example 1: How many terms of the series 1 + 3 + 9 +….sum to 121
(a) 18
(b)19
(c) 13
(d) 5
Ans: (d)
We know that,
In the given series,
a = 1,
r = 3/1 = 3,
S_{n} = 121
242 = (3^{n} – 1)
243 = 3^{n}
3^{5} = 3^{n}
n = 5
Example 2: Find Sum of given Geometric Series upto 9th term 7,14,28,56……
(a) 3177
(b) 3577
(c) 1377
(d) 5377
Ans: (b)
We know that,
In the given series,
a = 7,
r = 14/7 = 2
= 3577
Example 1: What is the geometric mean of 2, 3, and 6?
(a) 4.5
(b) 6.5
(c) 3.30
(d) 6.4
Ans: (c)
We know that,
GM = (abc)^{1/3}
Therefore, there Geometric Mean (GM) = (2 x 3 x 6)^{1/3}
= 3.30
Example 2: What is the geometric mean of 36 and 9?
(a) 24
(b) 16
(c) 18
(d) 14
Ans: (c)
We know that,
GM = (ab)1/2
Therefore, there Geometric Mean (GM) = (36 x 9)^{1/2}
= 18
314 videos170 docs185 tests

1. What is a geometric progression? 
2. How do you find the nth term of a geometric progression? 
3. Can the common ratio in a geometric progression be negative? 
4. How can geometric progressions be used in reallife situations? 
5. What is the sum of a geometric progression? 
314 videos170 docs185 tests


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