Question

If a,b,c are in A.P., prove that b+c, c+a, a+b are in A.P.​

Answer 1

Answer:

Step-by-step explanation:

If a, b, c are in ap

Then a+c/2=b

a+c=2c

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

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

2b=a+c

b=a+c/2

Proved

Answer 2

Answer:

$\huge \fbox \pink {Sσlutíσn}$

Given,a,b and c are in A.P.

To prove, b+c,c+a,a+b are in A.P.

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

⇒c+a-b-c=a+b-c-a

a-b=b-c

⇒b-a=c-b

∴ a,b and c are in A.P.

∴b+c,c+a,a+b are in A.P.