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Question

Which term of the geometric sequence,
(i) 5,2,45,825,...., is 12815625?
(ii) 1,2,4,8,...., is 1024?

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Solution

(i) The given geometric progression is 5,2,45,825,...... where the first term is a1=5, second term is a2=2 and so on.

We find the common ratio r by dividing the second term by first term as shown below:

r=25

We know that the general term of an geometric progression with first term a and common ratio r is Tn=arn1

Let the nth term of the given A.P be Tn=12815625 and substitute a=5 and r=25 in Tn=arn1 as follows:

Tn=arn112815625=5(25)n112815625×5=(25)n12756×5=(25)n12756+1=(25)n1
2757=(25)n1(25)7=(25)n17=n1n=7+1n=8

Hence, 8th term of the given G.P is 12815625.

(ii) The given geometric progression is 1,2,4,8,,...... where the first term is a1=1, second term is a2=2 and so on.

We find the common ratio r by dividing the second term by first term as shown below:

r=21=2

We know that the general term of an geometric progression with first term a and common ratio r is Tn=arn1

Let the nth term of the given A.P be Tn=1024 and substitute a=1 and r=2 in Tn=arn1 as follows:

Tn=arn11024=1(2)n1210=2n110=n1n=10+1n=11

Hence, 11th term of the given G.P is 1024.


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