# If a,b,c are in A.P. Prove that b+c,c+a,a+b are also in A.P.?

If a,b,c are in A.P. Prove that b+c,c+a,a+b are also in A.P.?

## 11 Answers

If a,b,c are in AP then 2b=a+c

We have to prove

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

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

so a+c=2b

Which is true

Hence proved

All the best.

AKASH GOYAL

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if a,b,c are in AP then

b-a=c-b

a+c=2b ...........1

now we have to prove that b+c,c+a,a+b are in AP,

let these are in AP then

(a+c)-(b+c)=(a+b)-(a+c)

(a+c)=2b

from eq 1 we have a+c=2b ,RHS=LHS

so these terms are also in AP...

**b=a+d ;**

**c=a+2d.**

*a+b=2a+d;*

*a+c=2a+2d;*

*b+c=2a+3d.*