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  • If a , b, c are in AP, then which of the following are also in A.P.Option: 1 <img alt="b+c,a+c,a+b" src="/latex-image/?b&plus;c%2Ca&plus;c%2C

If a , b, c are in AP, then which of the following are also in A.P.

Option: 1

b+c,a+c,a+b
 


Option: 2

a^{2},b^{2},c^{2}

 


Option: 3

a^{2}b,b^{2}c,c^{2}a


Option: 4

None of these


Answers (1)

best_answer

Method 1:

As a,b,c are in A.P multipling each term by (-1) will give a new AP so, -a,-b, -c are in AP.

Now adding (a+b+c) to each term will give a new AP

So, a+b+c-a,a+b+c-b,a+b+c-c are in AP

b+c,a+c,a+b  is an AP

 

Method 2:

To prove A,B,C in AP we need to prove that 2B -(A+C) =0

So for option (A)

2\left ( a+c \right )-\left ( b+c \right )-\left ( a+b \right )

=2a+2c-b-c-a-b

=0

 

Posted by

Shailly goel

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