Math 3 Unit 5 Day 2 Arithmetic/Geometric Series and Summation
A series is the ________________________________________________________________________________________________________.
 What is the difference between a sequence and a series?
Ex. What is the series for: 3, 6, 9, 12, 15, 18, 21, 24, 27
Finite Series Formulas:
Finite Arithmetic Series:
Finite Geometric Series:
Steps for Evaluating a Finite Series:
1. Determine if the terms in the series _____________________________________________________________________.
– Does it have ______________________________________________________________________________?
2. Substitute the information you are given into the appropriate formula.
Ex. 1. Evaluate a series with the terms 1, 7, 13, 19, 25 for the first 13 terms.
Ex. 2. Find the sum of the first 10 terms of the geometric series with a1 = 6 and r = 2.
Ex. 3. A philanthropist donates $50 to the SPCA. Each year, he pledges to donate 12 dollars more than the
previous year. In 8 years, what is the total amount he will have donated?
• Sum of an Infinite Geometric Series
Even though this series goes on forever, we can still find the sum of this series because it is convergent.
The following conditions must be true to use this formula:
1 1 1
8, 4, 2,1, , , ,...
2 4 8
 The series must be ____________________________

The series must be ____________________________

The series must be ____________________________
Formula for finding the Sum of an
Infinite Geometric Series
Examples:
1. Determine whether each infinite geometric series diverges or converges. If it converges, find the sum.
a) 48 + 12 + 3 + …
b) 4 + 8 + 16 + …
2. Evaluate each infinite geometric series
5. Determine the type of series (arithmetic or geometric). Determine if the series is infinite or finite.
Evaluate the series.
a) Evaluate 𝑆10 for 250, 100, 40, 16, …
b) Find the sum of 1 + 5 + 9 + ... + 49 + 53
c) Given the sequence: 2, 4, 6, 8, … Find the sum of the first 15 terms.
Summation Notation:
Instead of saying: “Find the sum of the series denoted by an = 3n + 2 from the 3rd term to 7th term,” they
made up a symbol to deal with it.
∑ 𝑚𝑒𝑎𝑛𝑠 ___________________
Summation Notation for “Find the sum of the series denoted by an = 3n + 2 from the 3rd term to 7th term”
Example 4: Evaluating Using Summation Notation
Writing Series in Summation Notation:
Step 1) Determine the explicit formula.
Step 2) Identify the lower and upper limits.
Step 3) Write the series in summation notation.
Ex 5. Use summation notation to write the series for the specified number of terms. 1 + 2 + 3 + …; n = 6
Ex 6. Use summation notation to write the series for the specified number of terms.
3 + 8 + 13 + 18 + …; n = 9
Ex 7. Use summation notation to write the series for the specified number of terms. 3 + 6 + 9 + …; n = 33
Ex. 8. Use summation notation to write the series for a infinite geometric series where the initial term is
10 and the common ratio is 0.75.