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Algebra 1 : Sequences

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Example Question #4 : How To Find The Nth Term Of An Arithmetic Sequence

The fourth and tenth terms of an arithmetic sequence are 372 and 888, respectively. What is the first term?

Possible Answers:

172

200

114

Correct answer:

114

Explanation:

Let be the common difference of the sequence. Then $a_{4} + 6d = a_{10}$ , or, equivalently,

$d = \frac{a_{10} - a_{4}}{6}= \frac{888 - 372}{6} = \frac{516}{6}= 86$

$a_{1} + 3d = a_{4 }$ , or equivalently,

$a_{1} = a_{4 }-3d = 372-3\cdot 86 = 114$

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Example Question #5 : How To Find The Nth Term Of An Arithmetic Sequence

The ninth and tenth terms of an arithmetic sequence are, respectively, 87 and 99. What is its first term?

Possible Answers:

Correct answer:

Explanation:

The common difference of the sequence is the difference of the tenth and ninth terms: d = 99-87 = 12 .

The ninth term of an arithmetic sequence with first term and common difference is a + 8d , so we set this equal to 87, set d=12 , and solve:

a + 8d = 87

$a + 8 \cdot12 = 87$

a + 96 = 87

a = 87 -96 = -9

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Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

The eighth and tenth terms of an arithmetic sequence are, respectively, 87 and 99. What is its first term?

Possible Answers:

Correct answer:

Explanation:

The eighth and tenth terms of the sequence are a +7d and a + 9d , where is the first term and is the common difference. We can find the common difference by subtracting the tenth and eighth terms and solving for :

a + 9d = 99

$\underline{a+7d = 87}$

2d= 12

$2d \div 2= 12 \div 2$

d=6

Now set eighth term a + 7d equal to 87, set d=6 , and solve:

a + 7d = 87

$a + 7\cdot 6= 87$

a + 42= 87

a + 42 -42= 87 -42

a=45

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Example Question #7 : How To Find The Nth Term Of An Arithmetic Sequence

Find the 100th term in the following arithmetic sequence

$4,\ 11,\18,\25,\32,\39,\46,...$

Possible Answers:

764

712

688

578

697

Correct answer:

697

Explanation:

Before we can figure out the 100th term, we need to find a rule for this arithmetic sequence. Remember, the general rule for this sequence is

x_n=a+d(n-1)

where represents the first number in the sequence, is the common difference between consecutive numbers, and is the -th number in the sequence.

In our problem, a=4 . Also, each time we move up from one number to another, the number increases by 7. Therefore, $\ d=7$ . So the rule for this sequence is written as

x_n=4+7(n-1)

Now that we found our rule, we can go on and figure out what the 100th term is equal to. For the 100th term, n=100 . Thus

$x_{100}=4+7(100-1)$

$x_{100}=4+7(99)$

$x_{100}=4+693$

$x_{100}=697$

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Example Question #8 : How To Find The Nth Term Of An Arithmetic Sequence

To find any term of an arithmetic sequence:

$a_{n}=a_{1}+(n-1)d$

Where $a_{1}$ is the first term, is the number of the term to find, and is the common difference in the sequence.

Find the 18th term of the following arithmetic sequence.

$\left \{ 2,5,8,11,14...\right \}$

Possible Answers:

Correct answer:

Explanation:

Start by finding the common difference, , in this sequence, which you can get by subtracting the first term from the second.

d=5-2=3

Then, using the formula given before the question:

$a_{18}=2+(18-1)3=2+(17)3=2+51=53$

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Example Question #9 : How To Find The Nth Term Of An Arithmetic Sequence

To find any term of an arithmetic sequence:

$a_{n}=a_{1}+(n-1)d$

Where $a_{1}$ is the first term, is the number of the term to find, and is the common difference in the sequence.

Find the 26th term of the following arithmetic sequence.

$\left \{ 101,92,83...\right \}$

Possible Answers:

124

Correct answer:

Explanation:

Start by finding the common difference in terms by subtracting the first term from the second.

d=92-101=-9

Then, fill in the rest of the equation given before the question.

$a_{26}=101+(26-1)-9=101+(25)-9$

=101+-225=-124

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Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

Given the the sequence below, what is the 11th term of the sequence?

1, 5, 9, 13, . . .

Possible Answers:

Correct answer:

Explanation:

The 11th term means there are 10 gaps in between the first term and the 11th term. Each gap has a difference of +4, so the 11th term would be given by 10 * 4 + 1 = 41.

The first term is 1.

Each term after increases by +4.

The n^th term will be equal to 1 + (n – 1)(4).

The 11th term will be 1 + (11 – 1)(4)

1 + (10)(4) = 1 + (40) = 41

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Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence

The second term of an arithmetic sequence is ; the fourth term is 10x - 32 . What is the first term?

Possible Answers:

2x - 16

-2x + 32

x + 16

Correct answer:

x + 16

Explanation:

The common difference between the terms is half that between the second and fourth terms - that is:

$\small \frac{(10x - 32) - 4x}{2} = \frac{6x - 32 }{2} = 3x - 16$

Subtract this common difference from the second term to get the first:

4x - (3x - 16) = 4x - 3x + 16 = x + 16

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Example Question #11 : Arithmetic Series

An arithmetic sequence is given by the formula $a_{n} = 4 + 3 n$ . What is the difference between $a_{13}$ and $a_{10}$

Possible Answers:

Correct answer:

Explanation:

You can either calculate the vaules of $a_{13}$ and $a_{10}$ and subtract, or notice from the formula that each succesive number in the sequence is 3 larger than the previous

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Example Question #13 : How To Find The Nth Term Of An Arithmetic Sequence

Consider the following arithmetic sequence:

3, 14, 25, 36, 47, ... , n

What is the 37th term?

Possible Answers:

399

289

366

410

388

Correct answer:

399

Explanation:

A simple way to find the nth term of an arithmetic sequence is to use the formula $a_{n} = a_{1} + (d)(n-1)$ .

Here, $a_{n}$ is the term you are trying to find, $a_{1}$ is the first term, and is the common difference. For this question, the common difference is .

$a_{n} = 3 + (11)(37-1)$

=3 + (11)(36)

=399

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Algebra 1 : Sequences

Study concepts, example questions & explanations for Algebra 1

All Algebra 1 Resources

Example Questions

Example Question #4 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #5 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #7 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #8 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #9 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #1 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #11 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #11 : Arithmetic Series

Example Question #13 : How To Find The Nth Term Of An Arithmetic Sequence

All Algebra 1 Resources

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