If the pth term of an A.P. is x and qth term is y, show that the sum of its p+q terms is `(p+q)/2(x+y+(x-y)/(p-q))`

If pth term of an A.P. is c and the qth term is d, what is the rth term ?

If (p+q)^(th) term of an A.P. is m and (p-q)th term is n, then the pth term is:

If pth term of a G.P. is P and its qth term is Q, prove that the nth term is ((P^(n-q))/(Q^(n-p)))^(1/(p-q)) .

If ‘a’ and ‘b’ are respectively the pth and qth terms of an A.P., show that the sum of (p + q) terms is (p+q)/2[(a + b) + (a- b)/(p - q)] .

In an A.P., of which a is the first term, if the sum of the first p terms is zero, show that the sum of the next q terms is (-a(p +q)q)/(p-1) .

In an A.P., if p^(th) term is 1/q and q^(th) term is 1/p , prove that the sum of first pq terms is 1/2(pq+1) , where p ne q .

The first term of an A.P. is 5 and 100th term is - 292. Find the 50th term of the A.P.