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+(q-p)c = 0 `

If p^(th), q^(th) and r^(th) terms of an A. P. are l, m, n, respectively, show that (q - r )l + (r -p)m +(p - q)n =0

The 5^(th), 8^(th) and 11^(th) terms of a G.P are p,q and s , respectively . Show that q^2 =ps .

If the p^("th"), q^("th") and r^("th") terms of a G.P. are a, b and c, respectively. Prove that a^(q – r) b^(r-p) c^(P - q) = 1.

If pth, qth, and rth terms of an A.P. are a ,b ,c , respectively, then show that (a-b)r+(b-c)p+(c-a)q=0

Sum of the first p, q and r terms of an A.P. are a, b and c, respectively. Prove that a/p(q-r)+b/q (r-p) +c/r (p-q)=0

If p^(th), q^(th), r^(th) and s^(th) terms of an A.P. are in G.P, then show that (p – q), (q – r), (r – s) are also in G.P.