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 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)

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.