Question

If a, b and c are in A.P. show that a + 4, b + 4 and c + 4 are in A.P.

Answer 1

a, b and c are in A.P.

`=>` b – a = c – b

`=>` 2b = a + c

Given terms are (a + 4), (b + 4) and (c + 4)

Now (b + 4) – (a + 4) = b – a

= `(a + c)/2 - a`

= `(a + c - 2a)/2`

= `(c - a)/2`

And (c + 4) – (b + 4) = c – b

= `c - (a + c)/2`

= `(2c - a - c)/2`

= `(c - a)/2`

Since (b + 4) – (a + 4) = (c + 4) – (b + 4), then the given terms are in A.P.