# Explict Formulas Arithmetic & Geometric

Find the next/missing numbers in each pattern.

1. 1,__,5,7,__,…

2. 2,4,6,8,__,__,__,…

3. 1,3,9,27,__,…

4. 1,-3,9,-27,__,…

5. 240,__,60,__,15,…

Coordinate Algebra

UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems?

Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5

Today’s Question: What is a Sequence? Is a sequence a function? Can you find the nth term and the domain of a sequence?

Standard: MCC9

12.R.IF.3

### Arithmetic Sequence

A sequence of terms that have a common difference between them

### Geometric Sequence

A sequence of terms that have a common ratio between them

Arithmetic or Geometric?

Example 1:

-22, -15, -8, -1, …

Arithmetic d = 7

Arithmetic or Geometric?

Example 2:

256, 64, 16, 4, …

Geometric r = 1/4

Arithmetic or Geometric?

Example 3:

7, 4, 1, -2, -5

Arithmetic d = -3

Arithmetic or Geometric?

Example 4:

4

3 9 81

,...

NEITHER

Arithmetic or Geometric?

Example 5:

NEITHER

## Explicit Formula

Formula used to find the n th term of a sequence

a n

a

1

n

 1

d

### Geometric Sequence

a n

 

n

 1

Find the common difference/ratio, the explicit formula, and the tenth term.

3, 9, 15, 21, …

a a n n

a

3

1

 

n n

 1

d

 

d = 6 a n

= 6n – 3

a

10

a

10

= 57

 3

Find the common difference/ratio, the explicit formula, and the seventh term.

a

3, 1.5, 0.75, 0.375, …

n

 

n

 1

r

1.5

3

 0.5

a n

 

n

 1

a

7

a

7

0.0456875

The fifth term is 1,792. The constant ratio is 4. Write the explicit formula.

a

5

 1792 and

n

 5 and

r

 4

a n

 

n

 1

1792 

a

1

1

a n

 

n

 1