What is the sum of the series 2, 4, 6, 8, 10...48. I never seem to get the right answer.

We can see that if we'll calculate the difference between
2 consecutive terms of the given series, we'll obtain the same value each
time:

4 - 2 = 6 - 4 = 8 - 6 = 10 - 8 = ...... =
2

So, the given series is an arithmetic progression whose
common difference is d = 2.

Now, we can calculate the sum
of n terms of an arithmetic progression in this way;

Sn =
(a1 + an)*n/2

a1 - the first term of the
progression

a1 = 2

an - the
n-th term of the progression

an =
48

n - the number of terms

 We
can notice that we know the first and the last terms but we don't know the number of
terms. We can calculate the number of terms using the formula of general
term.

an = a1 + (n-1)*d

48 = 2
+ (n-1)*2

We'll remove the
brackets:

48 = 2 + 2n -
2

We'll eliminate like
terms:

48 = 2n

We'll divide by
2:

n = 24

So, the number of
terms, from 2 to 40 is n = 24 terms.

S24 = (2 +
48)*24/2

S24 =
50*12

S24 =
600