In an A.P. (with usual notations):

(i) given a = 5, d = 3, a_n = 50, find n and S_n

(ii) given a = 7, a₁₃ = 35, find d and S₁₃

(iii) given d = 5, S₉ = 75, find a and a₉

(iv) given a = 8, a_n = 62, S_n = 210, find n and d

(v) given a = 3, n = 8, S = 192, find d.

The first term of an A.P. is 5, the last term is 45 and the sum is 400. Find the number of terms and the common difference.

The sum of first 15 terms of an A.P. is 750 and its first term is 15. Find its 20th term.

Find the sums given below:

(i) 34 + 32 + 30 + …. + 10

(ii) -5 + (-8) + (-11) + …. + (-230)