Q16 of 97 Page 199

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

Given that are in AP.

If are in AP

Adding 1 to each term

are in AP

Divide each term by

are in AP

Hence, a, b, c are in AP

Hence Proved.

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P.

Prove that P²Rⁿ = Sⁿ.

The p^th, q^th and r^th terms of an A.P. are a, b, c, respectively. Show that

(q – r )a + (r – p )b + (p – q )c = 0

If a, b, c, d are in G.P, prove that (aⁿ + bⁿ), (bⁿ + cⁿ), (cⁿ + dⁿ) are in G.P.

If a and b are the roots of x² – 3x + p = 0 and c, d are roots of x² – 12x + q = 0, where a, b, c, d form a G.P. Prove that (q + p): (q – p) = 17:16.