The sum S of the arithmetic sequence a, a + d, a + 2d, . . . , a + (n – 1)d is given by \small S=\frac{n}{2}\left [2a+(n-1)d \right ] . What is the sum of the integers from 1 to 100, inclusive, with the even integers between 25 and 63 omitted?

The required sum is 4214.

Step-by-step explanation:

We are given the following in the question:

An arithmetic sequence with first term a and common difference d.

The sum of n terms of A.P is given by

We have to find:

First series:

Second series:

The require sum is:

Thus, the required sum is 4214.