Quiz about Arithmetic and Geometric Sequences with Word Problems

Question 1

Which type of sequence is shown in the graph?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Question 2

Which sequence type, and common ratio/difference is correct for the table?

Accepted Answer

geometric

common ratio = 2

Answer

arithmetic

common ratio = 2

Answer

arithmetic

common difference = 2

Answer

geometric

common difference = -2

Question 3

Daisy received $2 on her first birthday. Each year, the amount of money she received tripled. How much money will she receive on her 5^th birthday?

Accepted Answer

$162

Answer

$10

Answer

$300

Answer

$416

Question 4

The local power company plans to raise rates to cover the increased cost of producing power. They determine the costs will increase by 4.2% per year for the next 10 years. If you paid a total of $1031.60 for power last year, what would you expect to pay for power over the next 10 years?
(Hint: Find a₁, a₁₀, and r)

Accepted Answer

$13,020.97

Answer

$10,316.00

Answer

$2,704.97

Answer

$12,220.97

Question 5

Calculate the sum of the first 15 terms of the arithmetic sequence where $$a_1 = 7$$ and $$d = 3$$ .

Accepted Answer

345

Answer

315

Answer

330

Answer

360

Question 6

Carey is organizing her books and putting them on shelves. She put 2 books on the first shelf, 8 books on the second shelf, 32 books on the third shelf, and 128 books on the fourth shelf. What kind of sequence is this?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Both

Answer

Neither

Question 7

Find the explicit formula for the sequence shown in the graph.

Accepted Answer

$$a_n=4\left(2\right)^{\left(n-1\right)}$$

Answer

$$a_n=4+2\left(n-1\right)$$

Answer

$$a_n=4\left(\frac{1}{2}\right)^{\left(n-1\right)}$$

Answer

$$a_n=2\left(4\right)^{\left(n-1\right)}$$

Question 8

Which type of sequence is shown in the graph?

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Question 9

You have $729 in the bank on Day 1, $243 on Day 2, and $81 on Day 3. Write the explicit formula that expresses the sequence.

Accepted Answer

a_n = 729(1/3)^n-1

Answer

a_n = 729(3)^n-1

Answer

a_n = 1/3(a_n-1)

Answer

a_n= 1/3(729)^n-1

Question 10

Explain how you could use a graphing calculator to determine whether the data in the table to the right represents a geometric sequence.

Accepted Answer

Divide each term by the preceding term to see if there is a common ratio.

Answer

Multiply each term by the preceding term to see if there is a common ratio.

Answer

Subtract each term from the preceding term to see if there is a common difference.

Answer

Add each term to the preceding term to see if there is a common difference.

Question 11

Remember that arithmetic sequences have a common difference (add/subtract). Geometric sequences have a common ratio (multiply/divide). SELECT the TWO true statements!

Accepted Answer

Arithmetic sequences have a common difference and we are adding the same number each time.

Accepted Answer

Geometric sequences have a common ratio and we are multiplying the same number each time.

Answer

Arithmetic sequences have a common difference and we are multiplying the same number each time.

Answer

Geometric sequences have a common ratio and we are adding the same number each time.

Question 12

Is this sequence arithmetic, geometric, or neither?
{26, 22, 18, 14, ...}

Accepted Answer

Arithmetic

Answer

Geometric

Answer

Neither

Question 13

What is the common difference in this sequence?{48, 32, 16, 0, ... }
[What are we adding to get to the next term?]

Accepted Answer

-16

Answer

1/2

Answer

2

Answer

-8

Question 14

Is this sequence Arithmetic, Geometric, or Neither?
{14, 22, 30, 38, .. }

Accepted Answer

Arithmetic

Answer

Geometric

Answer

Neither

Question 15

What is the common ratio in this sequence?
{96, 48, 24, 12, ... }

[Remember that we are MULTIPLYING to get from one term to the next.]

So $$\div$$ 8 would be the same as $$ imes\frac{1}{8}$$ .

Accepted Answer

1/2

Answer

2

Answer

12

Answer

24

Question 16

Which sequence is an arithmetic sequence?

Accepted Answer

3, 7, 11, 15, ...

Answer

3, 6, 2, 7, ...

Answer

3, 6, 12, 24, ...

Answer

3, 6, 10, 15, ...

Question 17

Which sequence is a geometric sequence with a common ratio of 2?

Accepted Answer

5, 10, 20, 40, ...

Answer

5, 3, 1, -1, ...

Answer

5, 7, 9, 11, ...

Answer

5, 15, 45, 135, ...

Question 18

Arithmetic, geometric, or neither?

100, 50, 25, 12.5, ...

Accepted Answer

Geometric

Answer

Arithmetic

Answer

Neither

Arithmetic and Geometric Sequences with Word Problems

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