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

2. 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

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

4. Write out and evaluate:55 66
163 60

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

7. Write each series using sigma notation:

9. Evaluate the sum of the finite Geometric Series
9.99

10. 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 ?