Staar Algebra Arithmetic and Geometric Sequences Creating Explicit Rules

Which kind of sequence has a common difference?

• Arithmetic
• Geometric

Which kind of sequence has a common ratio?

• Arithmetic
• Geometric

Which formula is used to find the explicit equation for geometric sequences?

• a_n = a_(n-1) + d
• a_n = a_(n-1) * r
• a_n = a₁ + d(n-1)
• a_n = a₁ * r^n-1

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
 -14, -11, -8, -5, ... 

• Arithmetic
  Common Difference: 3
• Arithmetic
  Common Difference: -3
• Geometric
  Common Ratio: 4
• Geometric 
  Common Ratio: 3

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
97, 86, 75, 64, ...

• Arithmetic
  Common Difference: 8
• Geometric
  Common Ratio: -11
• Arithmetic
  Common Difference: -11
• Geometric
  Common Ratio: -8

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
256, 64, 16, 4,... 

• Arithmetic
  Common Difference: 4
• Arithmetic 
  Common Difference: ¹/₄
• Geometric
  Common Ratio: -4
• Geometric 
  Common Ratio: ¹/₄

Identify whether the following sequence is Arithmetic or Geometric and identify the common ratio or difference:
-6, -18, -54...

• Arithmetic
  Common Difference: 3
• Geometric
  Common Ratio: -3
• Arithmetic
  Common Difference: 12
• Geometric
  Common Ratio: 3

What is the explicit rule for finding the nth term for the Geometric sequence:
-2, 12, -72, 432, ...

• a_n = -2(-6)^n-1
  
• a_n = -2 + 6(n-1)
• a_n = -6⋅a_n-1
  a₁ = -2
  
• a_n = a_(n-1) - 6
  a₁ = -2

What is the explicit rule for the Geometric sequence:
11, 22, 44, 88...

• a_n = 2(11)^n-1
• a_n = 11 + 2(n-1)
• a_n = 11(2)^n-1
• a_n = a_(n-1) + 11
  a₁ = 11

Find the next three terms in the geometric sequence. 

10, 20, 40, 80

• 90, 110, 130
• happy, dopey, sleepy
• 160, 320, 640
• 160, 360, 480