Quiz about Recursive Sequence

Question 1

Determine the 3rd term of the sequence.

a₁=5

a_n= 2a_n-1- 1

Accepted Answer

17

Answer

14

Answer

13

Answer

16

Question 2

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 3

Write a recursive formula for the following sequence: 10, 5, 0, -5,...

Accepted Answer

a₁= 10

a_n= a_n-1 - 5

Answer

a₁= 10

a_n= a_n-1 + 5

Answer

a₁= 10

a_n= a_n (5)

Answer

a₁= 10

a_n= a_n-1 (5)

Question 4

A formula that requires the computation of all previous terms to find the value of a_n.

Accepted Answer

Recursive Formula

Answer

Explicit Formula

Answer

Arithmetic Formula

Answer

Geometric Formula

Question 5

Find the first five terms.

Accepted Answer

$$-24,-18,-12,-6,\ 0$$

Answer

$$-18,-11,-4,\ 3,\ 10$$

Answer

$$-20,-13,-6,\ 1,\ 8$$

Answer

$$-18,-12,-6,\ 0,\ 6$$

Question 6

Find the common difference.

Accepted Answer

$$d=-4$$

Answer

$$d=-3$$

Answer

$$d=3$$

Answer

$$d=-2$$

Question 7

Which of the following equations is recursive?

Accepted Answer

f(n) = f(n-1) +4

Answer

f(n) = 2n - 5

Question 8

On a scale of 1-5, 1 meaning "I have no clue what is going on" to 5 meaning "I got it completely," how would you rate your understanding of recursive & explicit sequences

Accepted Answer

1

Accepted Answer

2

Accepted Answer

3

Accepted Answer

4

Accepted Answer

5

Question 9

What is the recursive rule for the sequence:
11, 22, 44, 88...

Accepted Answer

a_n = 2a_n-1

Answer

a_n = 2(11)^n-1

Answer

a_n = 11x 2

Answer

a_n = 11(2)^n-1

Question 10

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

Accepted Answer

1/2

Answer

2

Answer

-14

Answer

-7

Question 11

Given the first five terms, write the recursive formula.
15, 12, 9, 6, 3 ....

Accepted Answer

u₁ = 15
u_n = u_n-1 - 3

Answer

u₁ = 15
u_n = u_n-1 + 3

Answer

u₀ = 15
u_n = u_n-1 + 3

Answer

u₀ = 15
u_n = u_n-1 - 3

Question 12

Given the recursive formula below, find the explicit formula.
a₀= 1
a_n = a_n-1 + 5

Accepted Answer

a_n = 1 + 5n

Answer

a_n= 6 + 5n

Question 13

Given the recursive formula below, find the explicit formula.
a₁= 5
a_n = a_n-1 - 6

Accepted Answer

a_n = 11 - 6n

Answer

a_n = 5 - 6n

Question 14

Find the recursive formula for the sequence. $$1, 3, 9, 27,...$$

Accepted Answer

$$a_n=a_{n-1}\cdot3$$

Answer

$$a_n=a_{n-1}\cdot1+3$$

Answer

$$a_n=1\cdot3^{n-1}$$

Answer

$$a_n=3\cdot1^{n-1}$$

Recursive Sequence

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