Q19 of 102 Page 410

Find the sum of all odd integers from 1 to 201.

To Find: The sum of all odd integers from 1 to 201.

The odd integers form the following AP series:

1,3,5….201

First term = a = 1

Common difference = d = 2

Last term = 201

Let the number of terms be n

⇒1 + 2(n - 1) = 201

⇒n - 1 = 100

⇒n = 101

= 101 × 101 = 10201

The sum of all odd integers from 1 to 201 is 10201.

Thesumsof an terms of two arithmetic progressions are in the ratio (7n – 5) : (5n + 17). Show that their 6^th terms are equal.

If the ratio between the sums of n terms of two arithmetic progressions is (7n + 1) : (4n + 27), find the ratio of their 11^th terms.

Find the sum of all even integers between 101 and 199.

Find the sum of all integers between 101 and 500, which are divisible by 9.