Sequences (Unit 1)

What is a sequence?

A SEQUENCE is a set of numbers in a SPECIFIC ORDER.

What is an Arithmetic Sequence?

A sequence with a CONSTANT DIFFERENCE (d) between successive terms.

• Addition (constant)

• Subtraction (constant)

What is a Geometric Sequence?

A sequence with a CONSTANT RATIO (r) between successive terms.

• Multiplication (constant)

• Division (constant)

The sequence of an arithmetic function is ________________ with the constant difference between each term like the _______

Linear, slope (m=d)

What is the Arithmetic Explicit formula? (Esentially the function/ formula of an arithmetic function)

a{1} = the VALUE of the first term given in the sequence

n = the value’s PLACE within the sequence

(example: #80 is the third term in the sequence… n=3 for the value’s place within 80)

a{n} = a VALUE in the sequence, with respect to the nth term

When asked to solve for your term, you will need to solve for ___________

n

When asked to solve for your term, you will need to solve for ___________

The actual number/value sitting at a specific spot in the sequence.

“What term in the sequence is 297?” (Given a data set). Solve for ____

n

“Find the 130th term in the sequence” (Given a data set). Solve for ____

a{130}… solve for “y”

n=130. The question asks you to find the value of the 130nth term.

Fill in the blanks.

270, 90, 30, 10,…

t{5} = 270 ( r )^ (5-1)

r= (1/3)

What do you solve for first?

270, 90, 30, 10,…

t{n} = 270 ( 1/3 )^ (5-1)

1. (1/3 )^ (5-1)

2. (1/3 )^ (4) = (1/81)

3. 270 * (1/ 81) = (10/3)

Write a simplified explicit formula for the sequence.

7, 3, -1, -5,…

a{n} = 7 - 4(n-1)

—>

a{n} = 7-4n+1

—>

a{n} = 8 - 4n, n ≥ 1

Given the simplified explicit formula, what is missing?

a{n} = 8 - 4n

a{n} = 8 - 4, n ≥ 1

List the first two terms in each sequence.

b{n} = -5n +11, n ≥ 1

b{1} = -5(1) +11, n ≥ 1

= 6

b{1} = -5(2) +11, n ≥ 1

= 1

If the question asks this, fill in the blanks:

If the question gives you a number like 297 and asks what term it is, solve for _________.

If it gives you n and asks for the term, find__________.

n

a{n} ←find value

In this scenario,

b{n} = -5n +11, n ≥ __

1

**n here cannot be less than one!!

On a graph, your ______is your y-axis, and you ________is your x-axis.

Term Value = Y

Term Number (position in sequence) = X

Geometric Sequence:

Looking at the Geometric Sequence graph, we see that the graph forms an __________function.

The constant ratio between each term is like the ______of an exponential function.

Exponential

Base

Solve for n.