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SAT Math : Arithmetic Sequences

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Example Questions

Example Question #7 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

12.8, 17.2, 21.6 , ...

Give the sixteenth term of this sequence.

Possible Answers:

None of the other responses give the correct answer.

70.0

83.2

78.8

74.4

Correct answer:

78.8

Explanation:

Subtract the first term $a_{1}$ from the second term $a_{2}$ to get the common difference :

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

Setting $a_{1} = 12 .8$ and $a_{2} = 17.2$

d = 17.2 - 12.8 = 4.4

The th term of an arithmetic sequence $a_{n}$ can be found by way of the formula

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

Setting n = 16 , $a_{1} = 12 .8$ , and d = 4.4 in the formula:

$a_{16} = 12.8 + (16-1) 4.4$

$= 12.8 + 15 \cdot 4.4$

= 12.8 +66

=78.8

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Example Question #21 : Arithmetic Sequences

An arithmetic sequence begins as follows: 14, 27, 40...

What is the first four-digit integer in the sequence?

Possible Answers:

1,002

1,008

1,000

1,006

1,004

Correct answer:

1,002

Explanation:

Given the first two terms $a_{1}$ and $a_{2}$ , the common difference is equal to the difference:

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

Setting $a_{1} = 14$ , $a_{2} =27$ :

d = 27 - 14 = 13

The th term of an arithmetic sequence $a_{n}$ can be found by way of the formula

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

Since we are looking for the first four-digit whole number - equivalently, the first number greater than or equal to 1,000:

$a_{1}+ (n-1) d \ge 1,000$

Setting $a_{1} = 14$ and d = 13 and solving for :

$14 + (n-1) 13 \ge 1,000$

$14 + 13n-13 \ge 1,000$

$13n+1 \ge 1,000$

$13n+1 - 1 \ge 1,000 - 1$

$13 n \ge 999$

$13 n \div 13 \ge 999 \div 13$

$n \ge 76\frac{11}{13}$

Therefore, the 77th term, or $a_{77}$ , is the first element in the sequence greater than 1,000. Substituting n = 77 , $a_{1} = 14$ , and d = 13 in the rule and evaluating:

$a_{77}=a_{1}+ (n-1) d$

= 14+ (77-1) 13

$= 14+76 \cdot 13$

= 14+988

=1,002 ,

the correct choice.

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Example Question #33 : Sequences

$\small 2, 3, 5, 9, 17, x, 65, 129....$

$\small \textup{In the above number sequence, what is the value of}\,x?$

Possible Answers:

$\small 32$

$\small 33$

$\small 34$

$\small 35$

$\small 31$

Correct answer:

$\small 33$

Explanation:

Each term in the sequence is one less than twice the previous term.

So, $\small x=2\left ( 17\right )-1$

$\small x=33$

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Example Question #802 : Arithmetic

What is the next number in the following series: 0, 3, 8, 15, 24 . . . ?

Possible Answers:

Correct answer:

Explanation:

The series is defined by n² – 1 starting at n = 1. The sixth number in the series then equal to 6² – 1 = 35.

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Example Question #21 : Arithmetic Sequences

A sequence of numbers is as follows:

3, 8, 18, 38, 78, . . .

What is the sum of the first seven numbers in the sequence?

Possible Answers:

490

621

1529

719

248

Correct answer:

621

Explanation:

The pattern of the sequence is (x+1) * 2.

We have the first 5 terms, so we need terms 6 and 7:

(78+1) * 2 = 158

(158+1) * 2 = 318

3 + 8 + 18 +38 + 78 + 158 + 318 = 621

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

Find the next term of the following sequence:

267, 256, 245, 234, 223,...

Possible Answers:

212

213

More information is needed

210

211

Correct answer:

212

Explanation:

The sequence provided is arithmetic. An arithmetic sequence has a common difference between each consecutive term. In this case, the difference is ; therefore, the next term is 212 .

You can also use a formula to find the next term of an arithmetic sequence:

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

where the current term and d = the common difference.

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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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SAT Math : Arithmetic Sequences

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #7 : Nth Term Of An Arithmetic Sequence

Example Question #21 : Arithmetic Sequences

Example Question #33 : Sequences

Example Question #802 : Arithmetic

Example Question #21 : Arithmetic Sequences

Example Question #1 : 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 #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

All SAT Math Resources

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