Why do soaps not work in hard water?

If the sums of n terms of two APs are in ratio (2n + 3) : (3n + 2), find the ratio of their 10th terms.

The sum of n terms of an AP is 1/2 an^2 + bn. Find the common difference.

Write the sum of first n odd natural numbers.

In an AP, the pth term is q and (p + q)th term is 0. Show that its qth term is p.

The first and last terms of an AP are 1 and 11 respectively. If the sum of its terms is 36, find the number of terms.

What is the 10th common term between the APs 3, 7, 11, 15, 19, … and 1, 6, 11, 16, …?

If 7th and 13th terms of an AP be 34 and 64 respectively then find its 18thterm.

How many 2 – digit numbers are divisible by 7?

Find the 8th term from the end of the AP 7, 9, 11, …., 201.

How many terms are there in the AP 13, 16, 19, …., 43?

The 9th term of an AP is 0. Prove that its 29th term is double the 19th term.