Q7 of 176 Page 8

If a, b, c are in A.P., prove that
are in A.P.

Given: a, b, c are in AP

∴ b – a = c – b …(i)

To Prove: are in AP

⇒ b – a = c – b

∴a, b, c are in AP

are in AP

If are in A.P. and a + b + c ≠ 0, prove that are in A.P.

If a², b², c² are in A.P., show that are in A.P.

If a, b, c are in A.P., prove that

(b + c)² — a², (c + a)² — b², (a + b)² — c² are in A.P.

If a, b, c are in A.P., prove that

are in A.P.

If a, b, c are in A.P., prove thatare in A.P.