10.5 Recursive Geometric Formula

Type of sequence: ​ (a)  

This sequence has a common ​​ (b)   ​

The second term in the sequence is ​ (c)  

• geometric
• ratio
• 10
• arithmetic
• difference
• 7
• 2.5
• 3

Tags

AI.9.12.C

Which is the recursive formula describing this sequence?

• g_n = 2•3^n-1

• g₁ = 2

  g_n = 3 • g_n-1

• t_n = 2 + (n - 1)3

• a₁ = 2

  a_n = a_{n - 1} + 4

Tags

AI.9.12.D

g₅ = 3888 , and g₃ = 108.

The common ratio is ​ (a)   and the first term is ​ (b)  

• 6
• 3
• 1/2
• 1/6
• 0
• 1
• 160
• 2

Tags

AI.9.12.D

Given that the function f(x) = 4(2)^x models a geometric sequence, which statement is not true? (There may be more than one answer)

• The first term of the sequence is 8

• The first term of the sequence is 4

• The first term of the sequence cannot be determined

• The domain of the sequence is the counting numbers:

  {1, 2, 3, 4, ...}

Answer explanation

Since the domain is the counting numbers, the first term in the sequence is where x = 1: f(x) = 8

Tags

AI.9.12.C

A sequence can be generated by using a_n​= 3 • a_(n−1)​, where a_1​=4 and n is a whole number greater than 1. Which of the following terms are in the sequence?

Choose TWO correct answers

• 7

• 12

• 13

• 19

• 36

Tags

AI.9.12.C

A function representing a sequence is shown. Identify the type of sequence, the first term of the sequence, and the common ratio

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AI.9.12.C

A sequence is represented below.

{–2, –6, –18, –54,  –162 ...}

 Which recursive notation could be used to represent the sequence?

• a₁ = -2

  a_n = -3 • a_{n - 1}

• a₁ = -2

  a_n = a_{n - 1} – 4

• a₁ = 2

  a_n = -3 • a_{n - 1}

• a₁ = -2

  a_n = 3 • a_{n - 1}

Tags

AI.9.12.D

In a sequence of numbers, a₄ = 648, a₅ = 1944, a₆ = ​ 5832.

a₁ = ​ (a)  

a_n = (​ (b)   ) • a_{n - 1}

• 24
• 3
• 8
• 0
• 1/3
• 1296

Tags

AI.9.12.C

In a sequence of numbers, a₅ = 486, a₈ = ​ 13122.

a₁ = ​ ​ (a)  

a_n = (​ ​ (b)   ) • a_{n - 1}

• 6
• 3
• 2
• 0
• 1/3
• 12636
• 4212
• 18

Tags

AI.9.12.C

In a sequence of numbers, a₃ = 128, a₆ = ​ 8192.

a₁ = ​ (a)  

a_n = a_{n - 1} • ​ (b)  

• 8
• 4
• 2
• 0
• 1/4
• 8064
• 32
• 2688

Tags

AI.9.12.C