To find the sum of an arithmetic sequence, we need to know the first term, the common difference, and the number of terms.

The first term is 10 (the first integer divisible by both 2 and 5).

The common difference is 10 (since each term is 10 greater than the previous term).

To find the number of terms, we can use the formula for the nth term of an arithmetic sequence:

nth term = first term + (n - 1) * common difference

We want to find the largest n such that the nth term is less than or equal to 100.

100 = 10 + (n - 1) * 10

90 = (n - 1) * 10

9 = n - 1

n = 10

So there are 10 terms in the sequence.

The sum of an arithmetic sequence is given by the formula:

sum = (number of terms / 2) * (first term + last term)

sum = (10 / 2) * (10 + 100)

sum = 5 * 110

sum = 550

Therefore, the sum of the arithmetic sequence of integers from 1 to 100 that are divisible by both 2 and 5 is 550.