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

Find the sum of a 24–term arithmetic sequence where the first term is 12 and the last term is 219
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ruinsraidy4
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: $Sum=\frac{\left(12+219\right)\cdot 24}{2}$