1. Sequences & Series: Arithmetic, Geometric, Infinite!
Chapter 11
REVIEW
Sequences & Series:
Arithmetic, Geometric, Infinite!

2. Arithmetic Sequences Example: Write the explicit arithmetic rule.
2, 5, 8, 11, 14, …
nth term 1st term common difference

3. Arithmetic Series Example: Find the sum of the first 20 terms.…
1st term nth term

4. Geometric Sequences Example: Write the explicit geometric rule.
2, -6, 18, -54, 162, …
1st term common ratio

5. Geometric Series Example: Find the sum of the first 10 terms.…
1st term!!!

6. Infinite ∞ Geometric Series!
Example: Find the sum. …
but only if |r|<1

7. Summation Notation Let’s try it!
… means that we start with the first term and add all the way to the 7th term!
Let’s try it!

8. Recursive Rules Example: Write the recursive rule.
2, 5, 10, 50, 500, …
Arithmetic
Geometric

9. Example MC Questions
Which of the following expresses the series in summation notation?
A) B) C)
D) E)

10. Example MC Questions
Write the explicit formula for the nth term of the arithmetic sequence with a4 = 7 and a13 = 34.
A) 3n – 2 B) 3n – 5
C) 3n + 2 D) 3n + 5
E) none of these

11. Example MC Questions
Write the explicit formula for the nth term of the geometric sequence with a5 = 48 and r = 2.
A) 2n B) 2(3)n C) 2(3)n D) 3(2)n-1 E) 3(2)n-1

12. Example MC Questions
Which of the following gives the first 11 terms of the geometric series …
A) B) C)
D) E)