11.2 Arithmetic Series
represents the sum of the first terms of a series. (for ex., is the sum of the first 4 terms of a series)
Algebra 2 Intensified: 11.2 Day 2 Notes – Arithmetic Series
Warm­up: Find the 3 arithmetic means between and .
To develop a formula for the sum of any arithmetic series, consider the series below:
Now, write in two different orders (ascending and descending) and add the two equations together:
Definition: A series is an indicated sum of the terms of a sequence.
Arithmetic Sequence
18, 22, 26, 30
vs. Arithmetic Series
18 + 22 + 26 + 30
The sum of the first terms of an arithmetic series is given by
Example 2: Find the sum of the first 100 positive integers.
where is the first term, is the last term(nth term), and is the number of terms.
Example 1: Find the sum of the first 20 even integers beginning with 2.
Example 3: Find the first 3 terms of an arithmetic series in which
Example 4: Find the first 4 terms of an arithmetic series in which
1
11.2 Arithmetic Series
Sigma Notation
Ex: can be expressed in a more concise way using sigma notation as seen below:
Evaluating a sum in sigma notation
Example 5: Evaluate Example 6: Evaluate Example 7: Evaluate 2