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`

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 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

Answer each question by selecting the proper alternative from those given below each question so as to make each statement true : If pth and rth terms of an AP are a,b and c respectively. then a(q-r)+b(r-p)+c(p-q)

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.

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))

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 p^(th),q^(th)and r^(th) tern of G.P are a,b and c respectively then |{:(loga,p,1),(logb,q,1),(logc,r,1):}|=0

If the sum of p terms of an AP is q and the sum of q terms is p, then show that the sum of p+q terms is -(p+ q) . Alos, find the sum of first p-q terms (where, p gt q )

Let a,b,c,d be positive real numbers with altbltcltd . Given that a,b,c,d are the first four terms of an AP and a,b,d are in GP. The value of (ad)/(bc) is (p)/(q) , where p and q are prime numbers, then the value of q is