Arithmetic and Geometric Equations

• Sequence

• Recursive Formula

• Explicit Formula for an Arithmetic Sequence

• Explicit Formula for a Geometric Sequence

This is an arithmetic sequence. How many dots would be in the next figure?

• 4

• 13

• 14

• 15

What is the common ratio for the sequence:
28, 14, 7, 3.5...

• 2

• 1/2

• -14

• -7

Write a recursive formula for the following sequence: 10, 5, 0, -5,...

• a₁= 10

  a_n= a_n-1 - 5

• a₁= 10

  a_n= a_n-1 + 5

• a₁= 10

  a_n= a_n (5)

• a₁= 10

  a_n= a_n-1 (5)

Does the following represent a sequence that is arithmetic, geometric, or neither?

• Arithmetic

• Geometric

• Neither

Identify the generator in the following sequence: 
20, 40, 80, ...

• +20

• x2

• 10

Write an explicit equation for the following sequence:
9, 5, 1, ...

• t(n) = 13 - 4n 

• t(n) = 9 - 4n

• t(n) = -4 + 13n

Find the 40th term in the following sequence:
11, 18, 25, ...
Hint:  Write an explicit equation first.

• 284

• 291

• 280

Given the following sequence, is t(n) = -134 a possible term in the sequence?
-2, -7, -12, ...
Hint:  Use an explicit equation to help you.

• Yes

• No

Does the following represent a sequence that is arithmetic, geometric, or neither?
t(n) = 2(7)ⁿ

• Arithmetic

• Geometric

• Neither