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

##### 1 Answer

Feb 12, 2016

You use the formula

Where

#### 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:

**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: