# What is the sum of a 24–term arithmetic sequence where the first term is 12 and the last term is 219?

Feb 12, 2016

You use the formula $S u m = \frac{\left(F + L\right) \cdot n}{2}$
Where $n$=number of terms, $L$=last and $F$=first term

#### Explanation:

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:
Example :
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: $S u m = \frac{\left(12 + 219\right) \cdot 24}{2}$

Extra
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:
$S u m = \frac{F + L}{2} \cdot n$ (same result of course)