Quiz about arithmetic sequences recursive and explicit

Question 1

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 2

What formula is shown below?

$$a\left(n\right)=d\left(n-1\right)+a_1$$

Accepted Answer

Explicit Formula for Arithmetic Sequences

Answer

Explicit Formula for Geometric Sequences

Answer

Recursive Formula for Arithmetic Sequences

Answer

Explicit Formula for Geometric Sequences

Question 3

After looking at a sequence of numbers, you notice that the pattern is that 7 is added each time. What type of sequence is this?

Accepted Answer

Arithmetic Sequence

Answer

Geometric Sequence

Answer

Neither

Question 4

A sequence is given below. Select the explicit formula.

$$23,\ 21,\ 19,\ 17...$$

Accepted Answer

$$a\left(n\right)=-2n+25$$

Answer

$$a\left(n\right)=-2n+21$$

Answer

$$a\left(n\right)=23\cdot2^{n-1}$$

Answer

$$a\left(n\right)=23\cdot2^{n-1}$$

Question 5

What formula is shown below?

$$a\left(n\right)=a_{n-1}+d$$

Accepted Answer

Recursive Formula for Arithmetic Sequences

Answer

Explicit Formula for Arithmetic Sequences

Answer

Explicit Formula for Geometric Sequences

Answer

Explicit Formula for Geometric Sequences

Question 6

A sequence is given below. Select the explicit formula.

$$23,\ 21,\ 19,\ 17...$$

Accepted Answer

$$a\left(n\right)=-2n+25$$

Answer

$$a\left(n\right)=-2n+21$$

Answer

$$a\left(n\right)=23\cdot2^{n-1}$$

Answer

$$a\left(n\right)=23\cdot2^{n-1}$$

Question 7

Choose the answer that best describes the sequence shown below.

$$8,\ 4,\ 2,\ 1...$$

Accepted Answer

Geometric; common ratio 1/2

Answer

Arithmetic; common difference 4

Answer

Arithmetic; common difference -4

Answer

Geometric; common ratio 2

Answer

This is neither an arithmetic nor a geometric sequence.

Question 8

What is the recursive equation for this function?

Accepted Answer

f(0) = 5
f(x) = f(x-1) - 2

Answer

f(0) = 5
f(x) = f(x-1) + 2

Answer

f(0) = 5
f(x) = f(x-1) - 3

Answer

f(0) = 5
f(x) = f(x-1) + 3

Question 9

Choose the answer that best describes the sequence shown below.

$$3,\ 9,\ 15,\ 21...$$

Accepted Answer

Arithmetic; common difference 6

Answer

Arithmetic; common difference -6

Answer

Geometric; common ratio 3

Answer

Geometric; common ratio -3

Answer

This is neither an arithmetic nor a geometric sequence.

Question 10

After looking at a sequence of numbers, you notice that the pattern is that each number is multiplied by 3, then by 4, then by 5, and so on. What type of sequence is this?

Accepted Answer

Neither

Answer

Arithmetic Sequence

Answer

Geometric Sequence

Question 11

This is an arithmetic sequence. How many dots would be in the next figure?

Accepted Answer

13

Answer

4

Answer

14

Answer

15

Question 12

Identify the common difference.

-6, -3, 0, 3, 6....

Accepted Answer

d=3

Answer

d=4

Answer

d=-4

Answer

d=-3

Question 13

Identify the rule as recursive or explicit, then find the first 4 terms of the sequence.
a₁ = 100; a_n = a_n-1 - 8

Accepted Answer

Recursive; 100, 92, 84, 76

Answer

Explicit; 100, 92, 84, 76

Answer

Explicit; 100, 108, 116, 124

Answer

Recursive; 100, 108, 116, 124

Question 14

The first three terms of an arithmetic sequence are as follows

13, 19, 25

What are the next two terms of the sequence?

Accepted Answer

31 and 37

Answer

31 and 36

Answer

30 and 37

Answer

30 and 36

Question 15

Write and RECURSIVE FORMULA for the sequence...

2, 6, 10, 14...

Accepted Answer

f(1) = 2 ; f(n) = f( n-1) + 4

Answer

f(1) = 2 ; f(n) = f( n-1) * 4

Answer

f(1) = 2 ; f(n) = f( n-1) - 4

Answer

f(n) = 4n - 2

Question 16

Identify the common difference.

-6, -3, 0, 3, 6....

Accepted Answer

3

Answer

4

Answer

-4

Answer

-3

arithmetic sequences recursive and explicit

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