Arithmetic
Sum of Finite Series
When adding a small number of terms, the process used in the previous examples is effective. When the application requires the addition of a large number of terms, this process becomes too cumbersome and a formula will accelerate the process.Consider the sequence from the previos example.
1, 4, 7, 10, 13, 16
In this sequence, add terms 1 and 6, terms 2 and 5, and terms 3 and 4.
![SumFinite1 SumFinite1](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/594/Sequence_and_Series/Images/SumFinite1.png)
![SumFinite2 SumFinite2](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/594/Sequence_and_Series/Images/SumFinite2.png)
![SumFinite3 SumFinite3](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/594/Sequence_and_Series/Images/SumFinite3.png)
Notice each pair has the same sum and there are
of these sums.
![SumFinite4 SumFinite4](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/594/Sequence_and_Series/Images/SumFinite4.png)