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Question

State True or False. If a, b, c are in A.P., then b+c,c+a,a+b are also in A.P.

A
True
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B
False
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Solution

The correct option is A True
We have,
a,b,c are in A.P

So,
2b=a+c ............(1)

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

b+b+c+a=c+a+c+a

b+c+a+b=2(c+a)

2(c+a)=b+c+a+b

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

Hence, this is the answer. Hence the answer is True.

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