The first and the last terms of an A.P. are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference. (CBSE 2014)

If demotes the sum of the first n terms of an A.P., prove that S₃₀= 3 (S₂₀ – S₁₀). (CBSE 2014)

If the 10^th term of an A.P. is 21 and the sum of its first ten terms is 120, find its nth term. (CBSE 2014)

If the mth term of an A.P. is and the nth term is , then prove that the sum to mn terms is , where in m n. (CBSE 2015)

A manufacturer of TV sets produced 600 units in the 3rd year and 700 units in the 7th year. Assuming that, production increases uniformly by a fixed number of units every year. Find

(i) The production in 1^st year.

(ii) The production in 10^th year.

(iii) The total production in 7 years. (CBSE 2015)