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Question

The 11th,13thand15th terms of any G.P are in:


A

G.P

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B

A.P

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C

H.P

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D

A.G.P

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Solution

The correct option is A

G.P


Explanation for the correct option :

Step 1: Assumption

In Maths, Geometric Progression (GP) is a type of sequence where each succeeding term is produced by multiplying each preceding term by a fixed number, which is called a common ratio.

Let us consider the following G.P. with the initial term a and the common ratio r :

a,ar,ar2,ar3,,arn,

Step 2: Finding the 11th,13thand15th terms

The general term of the above G.P. will be: an=arn-1.

Therefore, we can write:

a11=ar10a13=ar12a15=ar14

Step 3: Checking whether these terms are in G.P.

Formula to be used: We know that the terms a,b,c are in G.P. if b2=ac.

Multiplying a11and a15, we get :

a11a15=ar10ar14=ar24=ar122=a132

Thus, the terms a11,a13 and a15are in G.P.

Hence, option (A) is the correct answer.


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