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  • If a,b,c are in A.P. 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%2

If a,b,c are in A.P. 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^2b,b^2c,c^2a


Option: 4

None of these


Answers (1)

best_answer

As a,b,c are in A.P.

Multiplying each term by (-1) will give a new A.P.

So, -a, -b, -c are in A.P.

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 is in AP.

b+c, a+c, a+b is an A.P. 

So option (1) is correct.

 

Method 2

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

So for option (A)

2(a+c)-(a+b)-(b+c)

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

=0

So option (A) is correct.

Posted by

Gunjita

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