Question

equations.
If a, b, c are in AP, show that b + C, C+ a, a + b, are also in AP.
CD​

Answer 1

Answer:

given that:

a, b, c are in A. P.

so, the common difference is same

d = b-a=c-b

2b=a+c eq. 1

let b+C, C+a, a+b are in A. P.

then, show that the common difference is same.

d = C+a-(b+C)

= C+a-b-C

= a-b

d=a+b-(C+a)

=a+b-C-a

=b-c

=b-(2b-a) [ from eq. 1 ]

=b-2b+a

=a-b

hence, the common difference are same.

then it is proved that b+C, C+a, a+b are in A. P.