Question

if a,b,c,are in ap prove that b+c,c+a,a+b are also in ap

Answer 1

Hey there,

If a,b,c are in AP then,

=>a+c=2b. ( b Is the AM between a and c)

Now for proving that

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

=>(b+c)+(a+b) must be equal to 2(c+a)

LHS=>

b+c+a+b=2b+(a+c)=2b+2b=4b.

RHS=>

2(a+c)=2(2b)=4b.

LHS=RHS .

Hence,b+c,c+a,a+b are in AP.

Hope it helps.

Answer 2

Answer:

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