13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…

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13.3 – Arithmetic and Geometric Series and Their Sums Objectives: You should be able to…

NOTE The difference between a series and a sequence is that a sequence is a list of terms, where a series is an indicated sum of the terms of sequence. In section 13.3 we will consider finite series and their sums.

Formulas The sum of the first n terms of an arithmetic series is:

Ex. Find S 50 of the arithmetic series… 5 + 10 + 15 + …

Formulas The sum of the first n terms of a geometric series is: Where r is the common ratio and r ≠ 1

Ex. Find the sum of... 3 + 9 + 27 +… + 6561

Find the sum of all positive 3-digit integers that are divisible by 8. Example:

Example: Find the sum of the first 10 terms of the geometric series 2 – 6 + 18 – 54 + …

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