Mathematics : Arithmetic Progressions

For what value of k will k+9, 2k-1 and 2k+7 are the consecutive terms of an A.P?

The 4th term of an A.P. is zero. Prove that the 25th term of the A.P. is three times its 11th term.

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.

The houses in a row 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 the sum of the numbers of houses following X.

In an AP, if S₅ + S₇ = 167 and S₁₀ = 235, then find the AP,  Where S_n denotes the sum of its first n terms.

The 14^th term of an AP is twice its 8^th term. If its 6^th  terms is -8, then find the sum of its first 20 terms.

Find the 60^th term of the AP 8, 10,12, ..., if it has a total of 60 terms and hence find the sum of its last 10 terms.

Find how many integers between 200 and 500 are divisible by 8.