If demotes the sum of first n terms of an A.P., prove that S₁₂ = 3 (s₈ – S₄). (CBSE 2015)

The sum of first 9 terms of an A.P. is 162. The ratio of its 6^th term to its 13^th term is 1:2. Find the first and 15^th term of the A.P. (CBSE 2015)

If the sum of first n terms of an A.P. is (3n² + 7n), then find its nth term. Hence write its 20^th term. (CBSE 2015)

The houses in a row are numbered consecutively from 1 to 49. Show that there exists a value of X such that sum of numbers of houses preceding the house numbered X is equal to sum of the numbers of houses following X. (CBSE 2016)

A thief, after committing a theft, runs at a uniform speed of 50 m/minute. After 2 minutes, a policeman runs to catch him. He goes 60 m in the first minute and increases his speed by 5 m/minute every succeeding minute. After how many minutes, the policeman will catch the thief? (CBSE 2016)