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 sum of the first four terms of an A.P. is 66. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

If , then show that a, b, c and d are in G.P.

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