• Turn in your Fall break Packet to the basket.
• 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
8 16 32
,...
3 9 81
NEITHER

Arithmetic or Geometric?
Example 5:
NEITHER

Formula used to find the n th term of a sequence

Explicit Formula for
Arithmetic Sequence a n
 a
1

 n  1
 d

Explicit Formula for
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