Question

If a,b,c are in AP then show that (b+c) , (c+a), (a+b) are also in AP.

Answer 1

Answer:

Step-by-step explanation:

In an AP difference is same

First term is b+c

Second term is c+a

Third term is a+b

a2-a1 = c+a-(b+c)

= c+a-b-c

= a-b -------->(1)

a3-a2 = a+b-(c+a)

= a+b-c-a

= b-c --------->(2)

a,b and c are in AP ( given)

So b-a=c-b

2b=a+c

2b-c=a

Put value of a in (1)

d1=a-b

= 2b-c-b=b-c

d1=d2

So they are in AP