Geometric and Recursive Sequences

Given the recursive formula, find the first four terms:
a_n = -3⋅a_n-1
a₁ = 45

• 45, -135, 405, -1215

• -45, -135, -405, -1215

• 45, 135, 405, 1215

• 45, 42, 39, 36

Tags

CCSS.HSF.BF.A.2

What is the recursive rule for the 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

Tags

CCSS.HSF.BF.A.2

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

Tags

CCSS.HSF.BF.A.2

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

Tags

CCSS.HSF.BF.A.2

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

Tags

CCSS.HSF.BF.A.2

Given the explicit formula, find the first four terms:
a_n = -400(¹/₂)^n-1

• -400, -200, -100, -50

• -400, 200, -100, 50

• -400, -399.5, -399, -398.5

• -400, -300, -200, -100

Tags

CCSS.HSF.BF.A.2

What is the explicit rule for the 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

Tags

CCSS.HSF.LE.A.2

What is the common ratio for the sequence:
3, 15, 75...

• 12

• 1/5

• 5

• 10

Tags

CCSS.HSF.BF.A.2

What kind of sequence is the pattern 400, 200, 100, 50, 25, ...?

• Arithmetic

• Geometric

• Neither

Tags

CCSS.HSF.BF.A.2

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

• 1/2 (or 0.5)

• - 1/2 (or -0.5)

• -14

• -7

Tags

CCSS.HSF.BF.A.2