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.

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.

Ram kali would need Rs.1800 for admission fee and books etc., for her daughter to start going to school from next year. She saved Rs.50 in the first month of this year and increased her monthly saving by Rs.20. After a year, how much money will she save? Will she be able to fulfill her dream of sending her daughter to school?

[CBSE2005,2014]

The first and the last terms of an AP are 7 and 49 respectively. If sum of all its terms is 420, find its common difference.

If demotes the sum of first n terms of an A.P., prove that S₁₂ = 3 (s₈ – S₄) .