Arithmetic
Arithmetic
Series Formula
Example 1
Find the sum of the first 50 terms of an arithmetic sequence whose first term is -5 and whose 50th term is -95.
and
Step 1. Determine a1 and an.
![SeriesFormulaEx1-1 SeriesFormulaEx1-1](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/596/Exponential_and_Logarithmic_Functions/Images/SeriesFormulaEx1-1.png)
![SeriesFormulaEx1-2 SeriesFormulaEx1-2](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/596/Exponential_and_Logarithmic_Functions/Images/SeriesFormulaEx1-2.png)
Step 2. Determine the number of pairs in the sequence.
![SeriesFormulaEx1-3 SeriesFormulaEx1-3](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/596/Exponential_and_Logarithmic_Functions/Images/SeriesFormulaEx1-3.png)
Step 3. To find the series, substitute and solve.
![SeriesFormulaEx1-4 SeriesFormulaEx1-4](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/596/Exponential_and_Logarithmic_Functions/Images/SeriesFormulaEx1-4.png)
![SeriesFormulaEx1-5 SeriesFormulaEx1-5](https://claregladwinresd.glk12.org/pluginfile.php/1011/mod_book/chapter/596/Exponential_and_Logarithmic_Functions/Images/SeriesFormulaEx1-5.png)