Free Printable Arithmetic and Geometric Sequences

1.

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

a)

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

b)

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

c)

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

d)

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

2.

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, ...

a)

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

b)

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

c)

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

d)

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

3.

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).

a)

200

b)

450

c)

1,015

d)

2,475

4.

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

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

a)

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

b)

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

c)

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

d)

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

5.

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

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

a)

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

b)

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

c)

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

d)

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

6.

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

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

a)

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

b)

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

c)

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

d)

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

7.

Arithmetic sequences form a linear equation.

Geometric sequences form an exponential equation.

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

a)

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

b)

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

c)

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

d)

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

8.

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

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

a)

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

b)

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

c)

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

d)

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

9.

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

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

a)

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

b)

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

c)

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

d)

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

10.

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.

a)

a₅ = 160

b)

a₅ = 40

c)

a₅ = 10

d)

a₅ = 80

11.

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

a)

20, 100, 500, 2500

b)

5, 20, 80, 320

c)

4, 20, 100, 500

d)

4, 9, 14, 19

12.

Which of the following best describes this sequence?

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

a)

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

b)

A geometric sequence with a common difference of 3.

c)

An arithmetic sequence with a common difference of 3.

d)

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

13.

Does the following table represent a geometric sequence or an arithmetic? Explain

a)

geometric, it has a constant rate

b)

geometric, it has a constant percentage

c)

arithmetic, it has a constant rate

d)

arithmetic, it has a constant percentage

14.

You have $10 in you bank account. It doubles every month. How much money will you have after 5 months?

a)

$50

b)

$35

c)

$320

d)

$250

15.

What is the eleventh term of an arithmetic sequence in which a1 = 3 and d = 6?

a)

63

b)

39

c)

69

d)

36

Arithmetic and Geometric Sequences

Total questions: 15

Worksheet time: 44mins

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