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Arithmetic

Series Formula

Example 2

The sum of the first 50 terms of an arithmetic sequence is 4,800. If the 50th term is 194, find the first term and the common difference.

Step 1. Determine a1 and an.
SeriesFormulaEx2-1 and SeriesFormulaEx2-2
Step 2. Determine the number of pairs that will make this sum.
SeriesFormulaEx2-3
Step 3. Substitute into the formula and solve.
SeriesFormulaEx2-4
SeriesFormulaEx2-5
SeriesFormulaEx2-6
The first term, a1, is -2.
 
Step 4. Determine the formula for the sequence.
SeriesFormulaEx2-7
SeriesFormulaEx2-8

Step 5. Solve for d.
SeriesFormulaEx2-9
SeriesFormulaEx2-10

The common difference is 4.