Algebra Patterns and Sequences
Presentation
•
Mathematics
•
10th Grade
•
Hard
Joseph Anderson
FREE Resource
7 Slides • 5 Questions
1
Mathematics 10
Prepared by: Mr. Renz Mark M. Ramos
2
generates patterns
illustrate an arithmetic sequence
solve problems involving sequence
Learning Objectives
3
If a sequence does not have a last term.
2, 4, 6, 8, 10, . . . , 2n, . . .
Infinite
is a list of numbers. The numbers in a sequence are called terms and are often written as
a1, a2, a3, ..., an, ...
Sequences
4
Find a possible formula for the nth term of a sequence whose first four terms are 5, 9, 13, 17, . . .
Formula: an = 4n + 1.
5
Find a possible formula for the nth term of a sequence whose first four terms are 7, 11, 15, 19, . . .
Formula: an = 4n + 3.
6
Multiple Choice
Find the possible formula for the nth term of a sequence whose first four terms are 11, 18, 25, 32, . . .
an = 7n + 3
an = 7n + 2
an = 7n + 4
7
Find the first three terms and the 11th term of the sequence defined by each formula
8
Fill in the Blanks
Find the first three terms of the sequence defined by
an = 2n3 - 2
9
Fill in the Blanks
Find the 16th term of the sequence defined by
bn = 5 + 2n
10
Recursion Formula
11
Multiple Choice
Find the first five terms of the sequence defined recursively.
a1 = 5; an = 3(an-1 - 2) for n≥2
a2 = 9
a3 = 20
a4 = 56
a5 = 152
a2 = 9
a3 = 21
a4 = 56
a5 = 162
a2 = 9
a3 = 21
a4 = 56
a5 = 152
12
Multiple Choice
Find the first five terms of the sequence defined recursively.
a1 = 1; an = 2an-1 + 1 for n≥2
a2 = 3
a3 = 7
a4 = 15
a5 = 31
a2 = 1
a3 = 3
a4 = 7
a5 = 31
a2 = 3
a3 = 7
a4 = 15
a5 = 30
Mathematics 10
Prepared by: Mr. Renz Mark M. Ramos
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