The pth and qth terms of an A.P. are x and y respectively. Prove that the sum of (p + q) terms is.
`(p+q)/(2)[x+y+(x-y)/(p-q)].`

The (p+q)th term and (p-q)th terms of a G.P. are a and b respectively. Find the pth term.

If the p^(t h) and q^(t h) terms of a G.P. are q and p respectively, show that (p+q)^(t h) term is ((q^p)/(p^q))^(1/(p-q)) .

The p^(t h) term of an A.P. is a and q^(t h) term is b Prove that the sum of its (p+q) terms is (p+q)/2{a+b+(a-b)/(p-q)}dot

(a) The 3rd and 19th terms of an A.P. are 13 and 77 respectively. Find the A.P. (b) The 5th and 8th terms of an A.P. are 56 and 95 respectively. Find the 25th term of this A.P. (c) The pth and qth terms of an A.P. are q and p respectively. Prove that its (p + q)th term will be zero.

If (p+q) ^(th) term and (p-q) ^ (th) terms of G.P. are a and b respectively, prove that p^(th) term is sqrt(ab)

If the sum of p terms of an A.P. is q and the sum of q terms is p, show that the sum of (p+q) terms is -(p+q).

The pth term of an A.P. is a and qth term is bdot Then find the sum of its (p+q) terms.

If the pth, qth and rth terms of an A. P. are in G.P., prove that the common ratio of the G.P. is (q-r)/(p-q) .

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

If the pth, th, rth terms of a G.P. are x, y, z respectively, prove that x^(q-r).y^(r-p) .z^(p-q) = 1 .