Find the sum of the even integers between 21 and 45

We know that
This is an arithmetic sequence with a1 = 21 and common difference, d = 2 [even integers]
The general formula for the n-th term of an arithmetic sequence is
 an = a1 + (n-1)d
So
 in this case we have
 an = 21 + (n-1)2 > an = 2n + 19

We need to find n for the last term, 45:
45 = 2n + 19 > 2n = 26 -> n = 13

The formula for the sum of the first n terms of a arithmetic sequence is
S = (n/2)(a1 + an)
S = (13/2)(21 + 45)> 429

the answer is
429