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. (CBSE 2014)

The sum of the first 7 terms of an A.P. is 63 and the sum of its next 7 terms is 161. Find the 28^th term of this A.P. (CBSE 2014)

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? (CBSE 2014)

If the ratio of the sum of first n terms of two A. P’s is (7n + 1) : (4n + 27), find the ratio of their m^th terms. (CBSE 2015)

The sums of first n terms of three arithmetic progressions are S₁, S₂ and S₃ respectively. The first term of each A.P. is 1 and their common differences are 1, 2 and 3 respectively. Prove that S₁ + S₃ = 2S₂. (CBSE 2016)