Question

If a,b,c,d,e are in AP. Prove that a+e=b+d= 2c

Answer 1

if a, b, c, d, e are arithmetic sequences:

b - a = c - b = d - c = e - d

---> c-b = d-c [the middle two]
rearrange: 2c = d+b

since

b - a = c - b = d - c = e - d

we know that b-a = e-d

--> b+d = a+e

thus.. 2c = d+b=a+e

I HOPE IT HELPS