Show:
Introduction to Sequences
Series and Summation Notation
Arithmetic Sequences and Series
Geometric Sequences and Series
Infinite Geometric Series
Ms. Young
100
Define Sequence
A sequence is an ordered set of numbers.
100
What is a series?
An indicated sum of the terms of a sequence.
100
What is an arithmetic sequence?
A sequence in which successive terms differ by the same number d called the common difference.
100
What is a geometric sequence?
A sequence in which the ratio of successive terms is a constant called the common ratio r.
100
What is an infinite geometric series?
A geometric series with infinitely many terms.
100

Ms. Young's favorite color.

What is blue?
200
Write and label the first 10 terms of the Fibonacci Sequence
a1 = 1, a2 = 1, a3 = 2, a4 = 3, a5 = 5, a6 = 8, a7 = 13, a8 = 21, a9 = 34, a10 = 55
200
Write an example of summation notation, and explain the three important pieces of information.
Answers will vary
200
What is an arithmetic series?
The indicated sum of the terms of an arithmetic sequence.
200
What is a geometric series?
The indicated sum of the terms of a geometric sequence.
200
For what values of the common ratio r do series converge? For what values of r do series diverge?
If |r| < 1, then the series is said to converge to a limit. If |r| > 1, then the series is said to diverge.
200

The church Ms. Young attends.

What is Good News Church?

300
Find the first 5 terms of the sequence an = 2^(n) - 3
a1 = -1 a4 = 13 a2 = 1 a5 = 29 a3 = 5
300
Find S(4) of the sequence 1/2, 1/4, 1/8, 1/16, ...
15/16
300
Determine if the sequence -3, 2, 7, 12, 17, ... is arithmetic. If so, give the common difference d.
Arithmetic, d = 5
300
Determine if the sequence 6, 10, 15, 21, ... is geometric. If it is, give the value of r.
The sequence 6, 10, 15, 21, ... is neither geometric nor arithmetic.
300
Determine whether the geometric series 20 + 24 + 28.8 + 34.56 + ... converges or diverges
Since r = 1.2, the series diverges.
300

The ministry Ms. Young volunteers for over the summer. 

What is Share the Love Ocala, Royal Family Kids Camp, and Teen Reach Adventure Camp?

400
Find the first 5 terms of the sequence with a1 = 5 and a(n) = 2a(n-1) + 1
a1 = 5 a2 = 11 a3 = 23 a4 = 47 a5 = 95
400
Question 2a on page 871
1 + 3 + 5 + 7 = 16
400
Find the 6th term of the arithmetic sequence with a9 = 120 and a14 = 195.
a6 = 75
400
Find the 10th term of the geometric sequence with a5 = 96 and a7 = 384
a10 = 3072
400
If it exists, find the sum of the infinite geometric series 5 + 4 + 3.2 + 2.56 + ...
S = 25
400

The number of schools Ms. Young has taught at.

What is 3?

500
Write a possible explicit rule for the nth term of the sequence 3, 6, 12, 24, 48, ...
3(2^(n-1))
500
Question 3b on page 872
120
500
Find S(16) for the arithmetic series 12 + 7 + 2 + (-3) + ...
S(16) = -408
500
Find S(7) for the geometric series 3 - 6 + 12 - 24 + ...
S(7) = 129
500
Question 2b on page 901
S = 2/3
500
Ms. Young's favorite band.

Who are twenty one pilots?