Q4 of 167 Page 19

If are in A.P., prove that:
are in A.P.

Since, are in AP,

a(b - c) = c(a - b)

Since, are in A.P.

Multiply in both denominator and numerator with,

C in LHS and a in RHS

Hence given terms are in AP

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

If a, b, c are in A.P., then show that:

(i) a²(b + c), b²(c + a), c²(a + b) are also in A.P.

(ii) b + c - a, c + a - b, a + b - c are in A.P.

(iii) bc – a², ca – b², ab – c² are in A.P.

If are in A.P., prove that:

bc, ca, ab are in A.P.

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

(a - c)² = 4 (a - b) (b - c)

If are in A.P., prove that:are in A.P.