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SAT Math : Sequences

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Example Questions

Example Question #5 : How To Find The Next Term In An Arithmetic Sequence

Solve each problem and decide which is the best of the choices given.

Find the sixth term in the following arithmetic sequence.
$\frac{1}{4},\frac{1}{8},0...$

Possible Answers:

$\frac{3}{8}$

$-\frac{1}{8}$

$-\frac{1}{4}$

$-\frac{3}{8}$

Correct answer:

$-\frac{3}{8}$

Explanation:

First find the common difference of the sequence,

$\frac{1}{4}-\frac{1}{8}=\frac{1}{8}$

$\frac{1}{8}-0=\frac{1}{8}$

Thus there is a common difference of

$\frac{1}{8}$ between each term,

so follow that pattern for another terms, and the result is $-\frac{3}{8}$ .

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Example Question #6 : How To Find The Next Term In An Arithmetic Sequence

Find the missing number in the sequence:

3, 9, 27, X , 243

Possible Answers:

112

Correct answer:

Explanation:

The pattern of this sequence is 3^n where represents the position of the number in the sequence.

3^n = 3^1 = 3 for the first number in the sequence.

3^2 = 9 for the second number.

3^3 = 27

For the fourth term, n=4 . Therefore, 3^4 = 81 .

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Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

$\sqrt{20} , \sqrt{180},...$

Express the next term of the sequence in simplest radical form.

Possible Answers:

$10 \sqrt{5}$

$9\sqrt{5}$

$20\sqrt{5}$

$18\sqrt{5}$

$36\sqrt{5}$

Correct answer:

$10 \sqrt{5}$

Explanation:

Using the Product of Radicals principle, we can simplify the first two terms of the sequence as follows:

$a_{1}=\sqrt{20} = \sqrt{4} \cdot \sqrt{5} = 2 \sqrt{5}$

$a_{2}= \sqrt{180} = \sqrt{36} \cdot \sqrt{5} = 6 \sqrt{5}$

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

$d = 6 \sqrt{5} - 2\sqrt{5} = ( 6 - 2 )\sqrt{5} = 4 \sqrt{5}$

Add this to the second term to obtain the desired third term:

$a_{3} = a_{2} +d = 6 \sqrt{5} + 4 \sqrt{5} =( 6 + 4) \sqrt{5} = 10 \sqrt{5}$ .

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Example Question #5 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

$\sqrt{5} , \sqrt{10},...$

Give the next term of the sequence in simplest radical form.

Possible Answers:

$3 \sqrt{5}$

$2 \sqrt{5}$

$\sqrt{15}$

None of the other choices gives the correct response.

$2 \sqrt{10}$

Correct answer:

None of the other choices gives the correct response.

Explanation:

Since no perfect square integer greater than 1 divides evenly into 5 or 10, both of the first two terms of the sequence are in simplest form.

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

Setting $a_{1}= \sqrt{5}, a_{2}= \sqrt{10}$ :

$d = \sqrt{10} - \sqrt{5}$

Add this to the second term to obtain the desired third term:

$a_{3} = a_{2} +d =\sqrt{10} + ( \sqrt{10} - \sqrt{5}) = \sqrt{10} + \sqrt{10} - \sqrt{5} = 2\sqrt{10}- \sqrt{5}$

This is not among the given choices.

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Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

$\frac{1}{5} , \frac{1}{3} , ...$

Give the sixth term of the sequence in decimal form.

Possible Answers:

$0.\overline{8}$

$0.9\overline{3}$

$0.8\overline{6}$

0.8

0.875

Correct answer:

$0.8\overline{6}$

Explanation:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

Setting $a_{1}= \frac{1}{5}, a_{2}= \frac{1}{3}$ :

$d = \frac{1}{3} - \frac{1}{5} = \frac{5}{15} - \frac{3}{15} = \frac{2}{15}$

The th term $a_{n}$ of an arithmetic sequence can be derived using the formula

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

Setting $n = 6 , a_{1} = \frac{1}{5}= \frac{3}{15}, d = \frac{2}{15}$ :

$a_{n} = \frac{3}{15} + (6-1) \cdot \frac{2}{15}$

$= \frac{3}{15} +5 \cdot \frac{2}{15}$

$= \frac{3}{15} + \frac{10}{15}$

$= \frac{13}{15}$

The decimal equivalent of this can be found by dividing 13 by 15 as follows:

Division

The correct choice is $0.8\overline{6}$ .

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Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

An arithmetic sequence begins as follows:

4, 5 i ,...

Give the sixth term of the sequence.

Possible Answers:

-16+25i

-20 + 30 i

20+25 i

-20 + 25i

25+30i

Correct answer:

-16+25i

Explanation:

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

$d = a_{2} - a_{1}$

Setting $a_{1}= 4, a_{2}= 5i$ :

d = 5i - 4 = -4+5i

The th term $a_{n}$ of an arithmetic sequence can be derived using the formula

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

Setting $a_{1}= 4, n = 6, d= -4+5i$

$a_{6} =4 + (6-1) ( -4+5i)$

=4 +5( -4+5i)

=4 +( -20+25i)

=(4 -20)+25i

=-16+25i

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Example Question #811 : Arithmetic

Complete the sequence:

1, 8, 27, x, 125

Possible Answers:

150

335

400

125

Correct answer:

Explanation:

The pattern of this sequence is n^3 where represents the place of each number in the order of the sequence.

Here are our givens:

n^3

1^3 = 1 , our first term.

2^3 = 8 , our second term.

3^3 = 27 , our third term.

This means that our fourth term will be:

4^3 = 64 .

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SAT Math : Sequences

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #5 : How To Find The Next Term In An Arithmetic Sequence

Example Question #6 : How To Find The Next Term In An Arithmetic Sequence

Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

Example Question #5 : How To Find The Next Term In An Arithmetic Sequence

Example Question #4 : How To Find The Next Term In An Arithmetic Sequence

Example Question #1 : How To Find The Next Term In An Arithmetic Sequence

Example Question #811 : Arithmetic

All SAT Math Resources

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