if a, b, c, are in a.p show that b+c, c+a,a+b are also in ap

Let a = a0, b = a0 + d and c = a0 + 2d.

Then b+c = 2a0 + 3d,         ... (1)

c+a = 2a0 + 2d                   .... (2)

a+b = 2a0 + d                     ...(3),

As we see the terms represented by 1, 2 and 3 are in AP with common difference d, and first term 2a0+d.

 

Regards,

Team,

TopperLearning.