Quiz about Arithmetic/Geometric Sequences

Question 1

What is the common difference of the sequence below?

6, 9, 12, 15, ...

Hint: Common difference means the ADDING pattern

Accepted Answer

3

Answer

6

Answer

9

Answer

12

Question 2

What is the first term of the sequence below?

6, 9, 12, 15, ...

Accepted Answer

6

Answer

3

Answer

9

Answer

12

Question 3

Now that we have found both the common difference and the first term of our sequence (6, 9, 12, 15, ...), we can write an EXPLICIT FORMULA for the arithmetic sequence.

Formula: $$a_n=a_1+d\left(n-1\right)$$

Hint: $$a_1=$$ first term & $$d=$$ common difference

Accepted Answer

$$a_n=6+3\left(n-1\right)$$

Answer

$$a_n=3+9\left(n-1\right)$$

Answer

$$a_n=9+3\left(n-1\right)$$

Answer

$$a_n=3+6\left(n-1\right)$$

Question 4

Using the formula $$a_n=a_1+d\left(n-1\right)$$ , where $$a_1$$ represents the first term and $$d$$ represents the common difference, write a formula for the sequence 18, 16, 14, 12, 10, 8, ...

Accepted Answer

$$a_n=18-2\left(n-1\right)$$

Answer

$$a_n=18+2\left(n-1\right)$$

Answer

$$a_n=2+18\left(n-1\right)$$

Answer

$$a_n=-2+18\left(n-1\right)$$

Question 5

What is the tenth term in the arithmetic sequence:

12, 19, 26, 33, ...

Hint: Find the common difference and then either continue the pattern or write and use an explicit formula.

Accepted Answer

75

Answer

47

Answer

61

Answer

96

Question 6

We have a sequence represented by the formula $$a_n=20+5\left(n-1\right)$$ . What is the 200th term?

Hint: The variable n represents term number. So here, n = 200.

Second Hint: Put in your calculator 20+5(200-1).

Accepted Answer

1,015

Answer

200

Answer

450

Answer

2,475

Question 7

Given the arithmetic sequence 10, 15, 20, ..., what is the 150th term?

Hint: Write an explicit formula and substitute 150 in for n.

Second Hint: The explicit formula for an arithmetic sequence is $$a_n=a_1+d\left(n-1\right)$$

Third Hint: The formula needs both the common difference (adding pattern) and the first term. Then n = 150.

Accepted Answer

755

Answer

530

Answer

685

Answer

820

Question 8

Write an explicit formula for the sequence 45, 40, 35, 30, ...

Hint: The sequence is arithmetic so use this formula: $$a_n=a_1+d\left(n-1\right)$$ .

Accepted Answer

$$a_n=45-5\left(n-1\right)$$

Answer

$$a_n=45+5\left(n-1\right)$$

Answer

$$a_n=5+45\left(n-1\right)$$

Answer

$$a_n=5-45\left(n-1\right)$$

Question 9

Write an explicit formula for the sequence 1.5, 2.0, 2.5, 3.0, ...

Hint: The sequence is arithmetic so use this formula: $$a_n=a_1+d\left(n-1\right)$$ .

Accepted Answer

$$a_n=1.5+0.5\left(n-1\right)$$

Answer

$$a_n=1.5-0.5\left(n-1\right)$$

Answer

$$a_n=0.5+1.5\left(n-1\right)$$

Answer

$$a_n=0.5-1.5\left(n-1\right)$$

Question 10

Write an explicit formula for the sequence -9, -7, -5, -3, ...

Hint: The sequence is arithmetic so use this formula: $$a_n=a_1+d\left(n-1\right)$$ .

Accepted Answer

$$a_n=-9+2\left(n-1\right)$$

Answer

$$a_n=-9-2\left(n-1\right)$$

Answer

$$a_n=2-9\left(n-1\right)$$

Answer

$$a_n=-2-9\left(n-1\right)$$

Question 11

Now we will look at our OTHER type of sequence...

We know arithmetic sequences have an adding pattern...

Well GEOMETRIC sequences have a MULTIPLYING pattern.

Given the sequence 3, 6, 12, 24, ..., what is the common ratio?

Hint: A common ratio is the sequence's multiplier.

Accepted Answer

2

Answer

4

Answer

6

Answer

8

Question 12

Arithmetic sequences form a linear equation.

Geometric sequences form an exponential equation.

Given the geometric sequence 2, 6, 18, ..., write an explicit formula.

Accepted Answer

$$a_n=2\left(3\right)^{n-1}$$

Answer

$$a_n=6\left(2\right)^{n-1}$$

Answer

$$a_n=2\left(6\right)^{n-1}$$

Answer

$$a_n=3\left(2\right)^{n-1}$$

Question 13

Given the geometric sequence 1, 5, 25, 125, ..., write an explicit formula.

Hint: The formula needed is $$a_n=a_1\left(r\right)^{n-1}$$ .

Accepted Answer

$$a_n=1\left(5\right)^{n-1}$$

Answer

$$a_n=5\left(5\right)^{n-1}$$

Answer

$$a_n=5\left(1\right)^{n-1}$$

Answer

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

Question 14

Given the geometric sequence 64, 16, 4, 1, ..., write an explicit formula.

Hint: The formula needed is $$a_n=a_1\left(r\right)^{n-1}$$ .

Second Hint: Similar to arithmetic sequences representing both adding AND subtracting patterns (because subtracting IS adding a negative)... geometric sequences represent both multiplying AND dividing patterns. Dividing is just multiplying by a reciprocal.

Accepted Answer

$$a_n=64\left(\frac{1}{4}\right)^{n-1}$$

Answer

$$a_n=64\left(4\right)^{n-1}$$

Answer

$$a_n=4\left(64\right)^{n-1}$$

Answer

$$a_n=\frac{1}{4}\left(64\right)^{n-1}$$

Question 15

Given the geometric sequence 80, 40, 20, 10, ..., write an explicit formula.

Hint: The formula needed is $$a_n=a_1\left(r\right)^{n-1}$$ .

Accepted Answer

$$a_n=80\left(\frac{1}{2}\right)^{n-1}$$

Answer

$$a_n=\frac{1}{2}\left(80\right)^{n-1}$$

Answer

$$a_n=80\left(2\right)^{n-1}$$

Answer

$$a_n=2\left(80\right)^{n-1}$$

Question 16

What is the fifth term for the sequence below?

$$a_n=5\left(2\right)^{n-1}$$

Hint: Use your calculator and replace n with 5.

Accepted Answer

a5 = 80

Answer

a5 = 160

Answer

a5 = 40

Answer

a5 = 10

Question 17

Find the first four terms of the sequence given the rule:
a_n = 4(5)^n-1

Accepted Answer

4, 20, 100, 500

Answer

20, 100, 500, 2500

Answer

5, 20, 80, 320

Answer

4, 9, 14, 19

Question 18

What is the 8th term in the geometric sequence below?

3, 9, 27, 81, ...

Accepted Answer

6,561

Answer

19,683

Answer

2,187

Answer

729

Question 19

Which of the following best describes this sequence?

$$\left\{135,\ 45,\ 15,\ 5,\ ...\right\}$$

Accepted Answer

A geometric sequence with a common ratio of $$\frac{1}{3}$$

Answer

An arithmetic sequence with a common ratio of $$\frac{1}{3}$$

Answer

A geometric sequence with a common difference of 3.

Answer

An arithmetic sequence with a common difference of 3.

Question 20

Which of the following best describes this sequence?

$$\left\{5,\ 8,\ 11,\ 14,\ ...\right\}$$

Accepted Answer

An arithmetic sequence with a common difference of 3.

Answer

An arithmetic sequence with a common ratio of 3.

Answer

A geometric sequence with a common difference of 3.

Answer

A geometric sequence with a common ratio of 3.

Arithmetic/Geometric Sequences

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