The first, second and last terms of an A.P. are a,b and c respectively, show that its sum is `((b+c-2a)(c+a))/(2(b-a))`

First , second and middle terms of an A.P. are a,b,c respectively . The sum of AP is :

The 4th, 7th and 10th terms of a GP. are a, b, c respectively. Show that b^2 = ac .

The first and last terms of an A.P. are a and l respectively. Show that the sum of nth term from the beginning and nth term from the end is a + l.

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

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

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

The first term of an A.P. is a, the second term is b and last term is c. Show that the sum of A.P. is : ((b+c-2a)(c+a))/(2(b-a)) .

a, b, c are in G.P. and x and y are the A.M.’s between a, b and b, c respectively. Show that : a/x+c/y=2 .

If ‘a’ is the first term, ‘d' the common difference and 'l' the last term of an A.P., then the sum of the series is : (l^2-a^2)/(2d)+1/2(a+l) .