Quiz about Recursive Formulas of Arithmetic and Geometric Sequences

Question 1

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

Accepted Answer

5

Answer

25

Answer

20

Answer

4

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

Which of the following recursive formulas represents the given sequence. 4, 12, 36, 108, 324, ...

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 4

Classify each function with its description. f\left(x\right)=f\left(x-1\right)+1,f\left(0\right)=5

Accepted Answer

arithmetic, recursive

Answer

arithmetic, explicit

Answer

geometric, explicit

Answer

geometric, recursive

Question 5

Decide what kind of sequence this is.
What is the recursive form for the following sequence
3, 15, 75, 375, 1875...

Accepted Answer

a_n= 5*a_n-1

Answer

a_n= (1/5)*a_n-1

Answer

a_n= a_n-1+5

Answer

a_n= a_n-1- 5

Question 6

What is the recursive formula for arithmetic sequences?

Accepted Answer

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

Answer

f(n) = f(1) + (n+1)d

Answer

f(n) = f(1) + nd

Answer

f(n) = f(1)+ (n-2)d

Question 7

Classify each function with its description. f\left(x\right)=f\left(n-1\right)+2,f\left(1\right)=4

Accepted Answer

arithmetic, recursive

Answer

arithmetic, explicit

Answer

geometric, explicit

Answer

geometric, recursive

Question 8

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 9

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

Question 10

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 11

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 12

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 13

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 14

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 15

Which of the following is a geometric sequence?

Accepted Answer

2, 6, 18, . . .

Answer

2, 4, 5, . . .

Answer

2, 4, 6, . . .

Answer

10, 20, 200, . . .

Question 16

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 17

The next term of the geometric sequence

4, 16, 64, ...

is

Accepted Answer

256

Answer

132

Answer

120

Answer

150

Question 18

Specifies the step by which each term of the sequence is generated from the preceding term or terms.

Accepted Answer

Recursive Formula

Answer

Sequence

Answer

Explicit Formula for an Arithmetic Sequence

Answer

Explicit Formula for a Geometric Sequence

Question 19

Write the recursive formula for 6, 17, 28, 39, 50....

Accepted Answer

a_n=a_n-1+11
a₁=6

Answer

a_n=a_n-1-4
a₁=6

Answer

a_n=a_n-1+9
a₁=6

Answer

a_n=a_n-1+6
a₁=6

Question 20

Write a recursive rule for the sequence 17, 1, -15, -31 . . .

Accepted Answer

a_n = a_n-1 - 16
a₁=17

Answer

a_n = a_n-1 + 16
a₁=17

Answer

a_n = a_n-1 - 17
a₁=17

Answer

a_n = a_n-1 - 15
a₁=17

Recursive Formulas of Arithmetic and Geometric Sequences

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