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 #Sum=((F+L)*n)/2#
Where #n#=number of terms, #L#=last and #F#=first term


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=((12+219)*24)/2#

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:
#Sum=(F+L)/2*n# (same result of course)