What is the sum of a 24–term arithmetic sequence where the first term is 12 and the last term is 219?
You use the formula
What you are actually doing (in your mind or on paper) is putting the sequence in a row and beneath that you put the same sequence in reverse order. Now when you add them vertically, two by two, you will get the same number (=first+last) every time:
1 2 3 4 5
5 4 3 2 1 +
6 6 6 6 6
This will be 6 x 5 = 30, because there are 5 terms here. But now you have added two sequences, so you have to divide by 2.
In your case:
Another way of putting it, would be to say you take the mean of first and last, and multiply that by the number of terms: