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

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 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.

The (m+n)^(th) and (m-n)^(th) terms of a G.P. are p and q respectively. Show that the m^(th) and n^(th) terms are sqrtpq and p((q)/(p))^((m)/(2n)) respectively.

If 10^(th) and 4^(th) terms of a G.P are 9 and 4 respectively, then its 7^(th) term is…….

If the 4^(th) and 7^(th) term of a G.P. are 27 and 729 respectively, then find the G.P.

If the 4th, 10th and 16th terms of a G.P. are x, y and z, respectively. Prove that x, y, z are in GP.

If the p th and qth terms of a GP are q and p respectively, then show that its (p+ q) th term is ((q^(p))/(p^(q)))^((1)/(p-q))

If m^(th), n^(th) and p^(th) terms of an A.P and G.P be equal and be respectively x,y, z then………...................................................... a ) x^(y).y^(z).z^(x) = x^(z).Y^(x).z^(y) b ) (x-y)^(x).(y-z)^(y)= (z-x)^(z) c ) (x-y)^(z) (y-z)^(x)= (z-x)^(y) d ) None of these

The sum of first p,q and r terms of an AP are a,b and c respectively . Show that (a)/p(q-r)+b/q(r-p)+c/r(p-q)=0

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