Arithmetic and Geometric Sequences

What is the 7th term of the geometric sequence defined by the rule

a_n = -3(2)^n-1 ?

• -96

• -384

• -7776

• -192

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

A sequence is defined by the recursive rule

a₁ = -4

a_n = a_n-1 + 5

What is the seventh term of the sequence?

• 8

• 31

• 7

• 26

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

A person dropped a penny from a platform at the top of a tall building. The distance the penny fell in feet during the n^th second of its descent can be found using the recursive rule a₁=16, a_n=a_n-1+32. How far did the penny fall during the fifth second?

• 112

• 176

• 144

• 96

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

Following the opening, the number of visitors to an art museum increased by 25% each month. The recursive rule

a₁= 1,024, a_n= 1.25_n-1 gives the number of visitors during the n^th month. How many people visited the museum during the fifth month?

• 5,120

• 2,000

• 3,125

• 2,500

The first three terms of an arithmetic sequence are 3, 11, and 19. Which function 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

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.2

A geometric sequence has as its first three terms 48, 12, and 3. Which function represents the sequence?

• a_n = 48(1/4)^n-1

• a_n = 48 - (n-1)36

• a_n = 48(4)^n-1

• a_n = 3(4)^n-1

Tags

CCSS.HSF.BF.A.2

CCSS.HSF.LE.A.2

A plumber charges $55 for 1 hour of work, $90 for 2 hours, and $125 for 3 hours. Which function represents the sequence of hourly charges?

• a_n = 55 + 35n

• a_n = 55(35)^n-1

• a_n = 35 + (n-1)55

• a_n = 55 + (n-1)35

Tags

CCSS.HSA.CED.A.1

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.1

CCSS.HSF.IF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

The fourth, fifth, and sixth terms of an arithmetic sequence are 56, 49, and 42. Which function represents the sequence?

• a_n = 56 - 7(n-1)

• a_n = 42 + 7(n-1)

• a_n = 77 - 7(n-1)

• a_n = 42(7)^n-1

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.3

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

An arithmetic sequence has a₁=2 and d=4. What is the Explicit Rule for a_n and use it to find the 20^th term.

• a_n = 2 - 4(n-1)

  a₂₀ = 82

• a_n = 2 + 4(n-1)

  a₂₀ = 78

• a_n = 2(4)^n-1

  a₂₀ = 2199023255552

• a_n = 4 + 2(n-1)

  a₂₀ = 42

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2

CCSS.HSF.IF.A.2

CCSS.HSF.LE.A.1

CCSS.HSF.LE.A.2

A geometric sequence has a₁ = 3 and r = 2. What is the Explicit Rule for a_n and use it to find the 10th term.

• a_n = 3 + 2(n-1)

  a₁₀ = 21

• a_n = 2(3)^n-1

  a₁₀ = 39366

• a_n = 3(2)^n-1

  a₁₀ = 1536

• a_n = 2 + 3(n-1)

  a₁₀ = 29

Tags

CCSS.HSF.BF.A.1

CCSS.HSF.BF.A.2