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SAT Math : Sequences

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Example Question #1941 : Psat Mathematics

Consider the following sequence of numbers:

2, 9, 16, 23, ...

What will be the 8^th term in the sequence?

Possible Answers:

Correct answer:

Explanation:

Each number in the sequence in 7 more than the number preceding it.

The equation for the terms in an arithmetic sequence is a_n = a₁ + d(n-1), where d is the difference.

The formula for the terms in this sequence is therefore a_n = 2 + 7(n-1).

Plug in 8 for n to find the 8^th term:

a₈ = 2 + 7(8-1) = 51

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Example Question #7 : Nth Term Of An Arithmetic Sequence

Find the seventh term in the following sequence:

3,17,31,45,...

Possible Answers:

101

115

Correct answer:

Explanation:

The difference between each term can be found through subtraction. For example the difference between the first and the second term can be found as follows:

17-3=14

One can check and see that this is the case for the other given numbers in the sequence as well.

In order to find the seventh term, expand the sequence by adding 14 to the last given number (4th number) and all of the following numbers until the 7th number in the sequence is reached.

This gives the sequence:

3,17,31,45,59,73,87

As seen above the seventh number in the sequence is 87 and the correct answer.

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Example Question #8 : Nth Term Of An Arithmetic Sequence

What is the tenth number in the sequence:

4, 7, 12, 19...

Possible Answers:

102

103

Correct answer:

103

Explanation:

The purpose of this question is to understand the patterns of sequences.

First, an equation for the $N^{th}$ term in the sequence must be determined ( $N^{2}+3$ ).

This is true because

N=1 will create 1^2+3=4 ,

N=2 will create 2^2+3=7 ,

N=3 will create 3^2+3=12 ,

N=4 will create 4^2+3=19 .

Then, the eqution must be applied to find the specified term. For the tenth term, the expression $10^{2}+3$ must be evaluated, yielding 103.

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Example Question #2 : How To Find The Nth Term Of An Arithmetic Sequence

You are given a sequence with the same difference between consecutive terms. We know it starts at and its 3rd term is . Find its 10th term.

Possible Answers:

Correct answer:

Explanation:

From the given information, we know -1+2x=5 , which means each consecutive difference is 3.

-1+9x=-1+9(3)=26

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Example Question #10 : 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:

78.8

74.4

70.0

83.2

None of the other responses give the correct answer.

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 #31 : Sequences

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

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

Possible Answers:

1,000

1,006

1,008

1,002

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

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

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

Possible Answers:

$\small 35$

$\small 32$

$\small 31$

$\small 33$

$\small 34$

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 #2 : How To Find The Next Term In An Arithmetic Sequence

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

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:

621

719

1529

248

490

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 #4 : 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:

213

More information is needed

211

212

210

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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SAT Math : Sequences

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1941 : Psat Mathematics

Example Question #7 : Nth Term Of An Arithmetic Sequence

Example Question #8 : Nth Term Of An Arithmetic Sequence

Example Question #2 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #10 : Nth Term Of An Arithmetic Sequence

Example Question #31 : Sequences

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

Example Question #2 : 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 #4 : How To Find The Next Term In An Arithmetic Sequence

All SAT Math Resources

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