Find the sum of all natural numbers lying between 100 and 1000, which are mutliples of 5.

Let the sum of n, 2n, 3n terms of an A.P., be S₁, S₂, S₃, respectively, show that

Find the sum of all the numbers between 200 and 400 which are divisible by 7.

Find the sum of all the two digit numbers, which when divided by 4, yields 1 as remainder.

Find sum of integers from 1 to 100 that are divisible by 2 or 5.

The sum of first 4 terms of an A.P. is 56. The sum of last 4 terms is 112. If its first term is 11, then find the number of terms.

The sums of first n terms of two A.P.’s are in the ratio of 14 – 4n : 3n + 5. Find the ratio of their 8th terms.

The ratio of sums of m and n terms of an A.P. is m² : n². Show that the ratio of with and nth term is 2m – 1 :2n – 1.

If S₁, S₂, S₃ ........S_p are the sums of n terms of p A.P.’s whose first terms are 1, 2,3, .....p and common differences are 1, 3, 5, .....(2p – 1) respectively. Show that

         

Insert 6 arithmetic means between 3 and 24.