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Arithmetic Series

Arithmetic Series. Lesson 8.3. Definitions. Series: an indicated sum of terms of a sequence Infinite Arithmetic series: goes on forever Arithmetic series: implies finite series. Sum the numbers 1, 2, … 100. Two formulas could be used:. ** Must have a constant difference!. Example 1.

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Arithmetic Series

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  1. Arithmetic Series Lesson 8.3

  2. Definitions • Series: an indicated sum of terms of a sequence • Infinite Arithmetic series: goes on forever • Arithmetic series: implies finite series

  3. Sum the numbers 1, 2, … 100 • Two formulas could be used: ** Must have a constant difference!

  4. Example 1 Evaluate: 0 + 3 + 8 + 15 + 24 + 35 + 48 + 63 196

  5. Example 2 Evaluate: (1 + 4 + 9 + 16 + 25 + 36 + 49 + 64) – 1 203

  6. Example 3 • A worker had to fill 100 boxes identically with machine tools. The shipper filled the first box in 13 minutes, but got faster by the same amount each time as time went on. If he filled the last box in 8 minutes, what was the total time that it took to fill the 100 boxes? • Distance is the same!! 1050 minutes  17.5 hours!

  7. Example 4 • A new business decides to rank its 9 employees by how well they work and pay them amounts that are in arithmetic sequence with a constant difference of $500 a year. If the total amount paid to the employees is $250,000, what will the employees make per year?

  8. Homework Pages 507 – 508 4 – 7, 10 – 11 13 – 15

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