Quiz about Explicit and Recursive Sequences Formulas

Question 1

Does this recursive routine model growth or decay, and by what percent?
U₁ = 10
U_n+1 = U_n*.75

Accepted Answer

Decay, 25%

Answer

Growth, 75%

Answer

Growth, 25%

Answer

Decay, 75%

Question 2

Given the sequence 11, 15, 19, 23..., which recursive formula describes it?

Accepted Answer

$$f\left(1\right)=11$$

$$f\left(n\right)=f\left(n-1\right)+4$$

Answer

$$f\left(1\right)=11$$

$$f\left(n\right)=f\left(n-1\right)+5$$

Answer

$$f\left(11\right)=1$$

$$f\left(n\right)=f\left(11\right)+4$$

Question 3

Given the sequence -5, -15, -25, -35..., which recursive formula describes it?

Accepted Answer

$$f\left(1\right)=-5$$

$$f\left(n\right)=f\left(n-1\right)-10$$

Answer

$$f\left(1\right)=-5$$

$$f\left(n\right)=f\left(n-1\right)+10$$

Answer

$$f\left(-5\right)=1$$

$$f\left(n\right)=f\left(-5\right)-10$$

Question 4

Which of the following recursive formulas represents the given sequence.

Accepted Answer

$$f\left(1\right)=4$$ , $$f\left(n\right)=f\left(n-1\right)\cdot3$$

Answer

$$f\left(1\right)=4$$ , $$f\left(n\right)=f\left(n-1\right)+8$$

Answer

$$f\left(1\right)=4$$ , $$f\left(n\right)=f\left(n-1\right)-8$$

Answer

undefined , $$f\left(n\right)=f\left(n-1\right)\cdot9$$

Question 5

Which of the following recursive formulas represents the given sequence. 7, 14, 28, 56, 112, ...

Accepted Answer

$$f\left(1\right)=7$$ , $$f\left(n\right)=f\left(n-1\right)\cdot2$$

Answer

$$f\left(1\right)=7$$ , $$f\left(n\right)=f\left(n-1\right)+7$$

Answer

$$f\left(1\right)=7$$ , $$f\left(n\right)=f\left(n-1\right)\cdot7$$

Answer

$$f\left(1\right)=7$$ , $$f\left(n\right)=f\left(n-1\right)+14$$

Question 6

Write the explicit formula for the sequence. 9, 5, 1, -3, ...

Accepted Answer

$$f\left(n\right)=9-4\left(n-1\right)$$

Answer

$$f\left(n\right)=9+5\left(n-1\right)$$

Answer

$$f\left(n\right)=4+9\left(n-1\right)$$

Answer

$$f\left(n\right)=9\cdot4^{\left(n-1\right)}$$

Question 7

Write the explicit formula for the sequence.

Accepted Answer

$$f\left(n\right)=216\cdot\left(\frac{1}{3}\right)^{\left(n-1\right)}$$

Answer

$$f\left(n\right)=8\cdot3^{\left(n-1\right)}$$

Answer

$$f\left(n\right)=216-144\left(n-1\right)$$

Answer

$$f\left(n\right)=216\cdot3^{\left(n-1\right)}$$

Question 8

Identify the common difference.
97, 86, 75, 64, ...

Accepted Answer

-11

Answer

8

Answer

11

Answer

-8

Question 9

What is the common ratio: 5, 25, 125, 625...

Accepted Answer

5

Answer

25

Answer

20

Answer

4

Question 10

Complete the table by looking for the pattern.

Accepted Answer

30, 10, 3.3, 1.1

Answer

30, 10, 3, 0

Answer

60, 30, 10, 0

Question 11

Find the missing terms of the arithmetic and geometric sequences in the table. Use the formulas.

Accepted Answer

10, 16, 22

Answer

8, 14, 20

Answer

12, 18, 24

Question 12

Find the missing terms of the arithmetic and geometric sequences in the table. Use the formulas.

Accepted Answer

22, 32, 52

Answer

20, 30, 50

Answer

18, 24, 36

Question 13

Find the missing terms of the arithmetic and geometric sequences in the table. Use the formulas.

Accepted Answer

8, 16, 32

Answer

8, 12, 16

Answer

12, 36, 64

Question 14

Find the missing terms of the arithmetic and geometric sequences in the table. Use the formulas.

Accepted Answer

-12, 48, 768

Answer

12, 48, 768

Answer

34, 48, 192

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