If the first, second and `nth` terms of a `A.P.` are respectively `a, b` and `c` then prove that the sum of `n` terms of this series is

If the first terms, second term and the last term of an A.P. are respectively a,b and c.Prove that the sum of the series is [(a+c)(b+c-2a)]/[2(b-a)] .

If the first, second and the last terms of an A.P. are a,b,c respectively, then the sum of the A.P. is

If the first, second and the last terms of an A.P. are a,b,c respectively, then the sum of the A.P. is

The first, second and last terms of an A.P. are a, b, c respectively, then the sum to first n terms is

If the sums of the first 8 and 19 terms of an A.P. are 64 and 361 respectively, find (i) the common difference and (ii) the sum of n terms of the series.

The first,second and middle terms of an AP are a,b,c respectively.Their sum is

If the first, second and last terms of A.P. be a, b, and c respectively, show that the sum of all terms of the A.P. is ((a+c)(b+c-2a))/(2(b-a)) .

If the first second and third term of AP are a,b and 2 a respectively.Then the sum of the AP is

The first, second and middle terms of an A.P. are a, b, c, respectively. Then the sum of all terms of the A.P. is