Number Patterns and Sequences

Patterns and Sequences

Mathematics 10
Prepared by: Mr. Renz Mark M. Ramos

• generates patterns

• illustrate an arithmetic sequence

• solve problems involving sequence

Learning Objectives

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, ..., a_n, ...

Sequences

Patterns and Sequences

Example 1

Find a possible formula for the nth term of a sequence whose first four terms are 5, 9, 13, 17, . . .

Formula: a_n = 4n + 1.

Example 2

Find a possible formula for the nth term of a sequence whose first four terms are 7, 11, 15, 19, . . .

Formula: a_n = 4n + 3.

Multiple Choice

Find the possible formula for the nth term of a sequence whose first four terms are 11, 18, 25, 32, . . .

• a_{n = 7n + 3}

• a_{n = 7n + 2}

• a_{n = 7n + 4}

Example 3

Find the first three terms and the 11th term of the sequence defined by each formula

Fill in the Blank

Find the first three terms of the sequence defined by

a_n = 2n³ - 2

,

,

Fill in the Blank

Find the 16th term of the sequence defined by

b_n = 5 + 2ⁿ

Recursion Formula

Multiple Choice

Find the first five terms of the sequence defined recursively.

a₁ = 5; a_n = 3(a_n-1 - 2) for $$n\ge2$$

• a₂ = 9
  a₃ = 20
  a₄ = 56
  a₅ = 152

• a₂ = 9
  a₃ = 21
  a₄ = 56
  a₅ = 162

• a₂ = 9
  a₃ = 21
  a₄ = 56
  a₅ = 152

Multiple Choice

Find the first five terms of the sequence defined recursively.

a₁ = 1; a_n = 2a_n-1 + 1 for $$n\ge2$$

• a₂ = 3
  a₃ = 7
  a₄ = 15
  a₅ = 31

• a₂ = 1
  a₃ = 3
  a₄ = 7
  a₅ = 31

• a₂ = 3
  a₃ = 7
  a₄ = 15
  a₅ = 30