Lesson 3-1 Geometric Series

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Presentation transcript:

Lesson 3-1 Geometric Series Secondary Math 3 Lesson 3-1 Geometric Series

Vocabulary Sequence: a list of numbers 𝑎 1 , 𝑎 2 , 𝑎 3 , 𝑎 4 ,…, 𝑎 𝑛 , … 𝑎 1 is the first term, and 𝑎 𝑛 is the 𝑛𝑡ℎ term or general term of the sequence Finite Sequence: A sequence that contains a first and last term Infinite Sequence: A sequence that has a first term, but continues without end. Series: 𝑆= 𝑎 1 + 𝑎 2 + 𝑎 3 + 𝑎 4 +…+ 𝑎 𝑛 +…, is the sum of a sequence. Can be Finite or infinite. Geometric Series: the sum of the terms of a geometric sequence. 𝑆=𝑎+𝑎𝑟+𝑎 𝑟 2 +𝑎 𝑟 3 +…+𝑎 𝑟 𝑛 +… 𝑎 is the first term and 𝑟 is the common ratio

Notation: Upper Limit 𝑘=3 7 𝑘 3 Explicit Formula Lower Limit

Write out and evaluate: 55 66 163 60

Warm Up: Find the equation for each geometric sequence: 6, 12, 24, 48, . . . . b. 100, 10, 1, 1 10 , . . . Find the Sum of the series: 𝑛=1 4 3𝑛+1

Write each series using sigma notation:

Evaluate the sum of the finite Geometric Series 9.99

A Professional Basketball Player Signed a contract for 3,000,000 dollars for the 1st year and a 3% increase every year after. How much will he earn in the first 5 years of his contract ?