Arithmetic and Geometric Sequences

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CCSS.HSF.BF.A.2

Arithmetic sequences form a linear equation.

Geometric sequences form an exponential equation.

Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

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CCSS.HSF.BF.A.2

• a₅ = 160
• a₅ = 40
• a₅ = 10
• a₅ = 80

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CCSS.HSF.BF.A.2

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

• 20, 100, 500, 2500
• 5, 20, 80, 320
• 4, 20, 100, 500
• 4, 9, 14, 19

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CCSS.HSF.BF.A.2

What is a₅ for the sequence below?

a_n = 5 ⋅ 2^(n-1) 

• a₅ = 160
• a₅ = 40
• a₅ = 10
• a₅ = 80

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CCSS.HSF.BF.A.2

The first three terms of an a sequence are 3, 11, and 19. Which formula represents the sequence?

• a_n = 8 + 3(n-1)

• a_n = 8(3)^n-1

• a_n = 3 + 8(n-1)

• a_n = 3 + 8n

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CCSS.HSF.BF.A.2

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)

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CCSS.HSF.BF.A.2

Write the recursive formula for 6, 17, 28, 39, 50....

• a_n=a_n-1+11
  a₁=6
• a_n=a_n-1-4
  a₁=6
• a_n=a_n-1+9
  a₁=6
• a_n=a_n-1+6
  a₁=6

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CCSS.HSF.BF.A.2

Given the recursive formula, find the first four terms:
a_n = a_n-1 + 5
a₁ = -16

• -16, -21, -26, -31
• 5, -11, -27, -43
• -16, -80, -500, -200
• -16, -11, -6, -1

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CCSS.HSF.BF.A.2

• 6, 24, 96, 384

• 6, 10, 14, 18

• 6, 20, 100, 500

• 6, 20, 76, 300

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CCSS.HSF.BF.A.2