What is the `n^(th)` term of an A.P. whose first term is 'a' and common difference is 'd'?

If a_n is the n^(th) term of an A.P whose first term is a and common difference is d, prove that n=(a_n-a)/d+1

What is the sum of first n terms of an A.P. whose first term is 'a' and common difference is 'd'?

If S_1,S_2 and S_3 are respectively the sums of n, 2n and 3n terms of an A.P, whose first term is a and common difference d, then find S_1,S_2 and S_3

Find the 10^th term of an AP whose nth term is (2n-3)/6 .

Find the 12^(th) term of a G.P. whose 8^(th) term is 192 and the common ratio is 2.

In an arithmetic sequence, m times the n^(th) term is equal to n times the m^(th) term. Prove that. its first term and common difference are equal.

Suppose that the first and the 5^(th) terms of an A.P. are-14 and 2 respectively Find the common difference of the A.P

In an A.P. the difference between the last and the first terms is 632 and the commons difference is 4. Then the number of terms in the A.P. is

The common difference of the arithmetic sequence 15, 14, 13, 12,......is 14-15=-1. First term of the sequence is 15 and the 15^(th) term is 15 + 14 xx-1= 15-14=1 . Similarly the 4^(th) term is 12 and the 12^(th) term is 4. Its 16^(th) term is x_16 = 15 + 15xx-1= 15-15 = 0 . So the sum of the first 31 terms is also zero. That is if then n^(th) term of an arithmetic sequence with common difference -1 is m, then the m^(th) term is n and the (m + n)^(th) term is zero. 7^(th) term of an arithmetic sequence is 10 and the 10^(th) term is 7. What is the common difference?

If S_(n) denotes the sum of first n terms of an A.P whose first term is a and (S_(nx))/(S_(x)) is independent of x then S_(p)=