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
