Question

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

Answer 1

a, b and c are in A.P.

`=>` b – a = c – b

`=>` 2b = a + c

Given terms are 4a, 4b and 4c

Now 4b – 4a = 2(2b – 2a)

= 2(a + c – 2a)

= 2(c – a)

And 4c – 4b = 2(2c – 2b)

= 2(2c – a – c)

= 2(c – a)

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