13.3 – Arithmetic and Geometric Series and Their Sums

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Essential Question: What is a sequence and how do I find its terms and sums? How do I find the sum & terms of geometric sequences and series?

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Presentation transcript:

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 SUM OF FINITE ARITHMETIC SERIES The sum of the first n terms of an arithmetic series is:

Ex. Find S50 of the arithmetic series… 5 + 10 + 15 + …

Formulas SUM OF FINITE GEOMETRIC SERIES 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

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

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