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SSAT Upper Level Math : Arithmetic Sequences

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Example Questions

Example Question #7 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

$1 \frac{1}{7}, 3 \frac{1}{4},...$

Which of the following is the first term greater than 100?

Possible Answers:

The forty-eighth term

The forty-ninth term

The fifty-first term

The forty-seventh term

The fiftieth term

Correct answer:

The forty-eighth term

Explanation:

The common difference of the sequence is

$3 \frac{1}{4} - 1 \frac{1}{7} = 2\frac{3}{28}$

so the th term of the sequence is

$a_{n} = 1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1)$

To find out the minimum value for which $a_{n} > 100$ , set up this inequality:

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) (n-1) > 100$

$1\frac{1}{7} + \left ( 2\frac{3}{28} \right ) n -2\frac{3}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n - \frac{27}{28} > 100$

$\left ( 2\frac{3}{28} \right ) n > 100 \frac{27}{28}$

$n > 100 \frac{27}{28} \div 2\frac{3}{28} = 47 \frac{54}{59}$

The correct response is the forty-eighth term.

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Example Question #3 : How To Find The Nth Term Of An Arithmetic Sequence

The tenth and twelfth terms of an arithmetic sequence are 8.4 and 10.2. What is its first term?

Possible Answers:

0.9

1.2

1.8

0.3

-0.6

Correct answer:

0.3

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

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

Since the tenth and twelfth terms are two terms apart, the common difference can be found as follows:

$a_{10}+2d=a_{12}$

8.4+2d=10.2

8.4+2d- 8.4=10.2 - 8.4

2d=1.8

d = 0.9

Now, we can set n = 10, d = 0.9 in the sequence equation to find $a_{1}$ :

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

$a_{10} = a_{1}+ (10-1)0.9$

$8.4 = a_{1}+ 9 \cdot 0.9$

$8.4 = a_{1}+ 8.1$

$8.4 - 8.1 = a_{1}+ 8.1 - 8.1$

$a_{1} = 0.3$

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Example Question #10 : How To Find The Nth Term Of An Arithmetic Sequence

The eleventh and thirteenth terms of an arithmetic sequence are, respectively, 11 and 14. Give its first term.

Possible Answers:

$-5\frac{1}{2}$

$-2\frac{1}{2}$

$1\frac{1}{2}$

Correct answer:

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

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

Since the eleventh and thirteenth terms are two terms apart, the common difference can be found as follows:

$a_{11}+2d=a_{13}$

11+2d=14

11+2d -11=14 -11

2d = 3

$d = \frac{3}{2}$

Now, we can set $n = 11, d =\frac{3}{2}$ in the sequence equation to find $a_{1}$ :

$a_{11} = a_{1}+ (11-1) \frac{3}{2}$

$11= a_{1}+ 10 \cdot \frac{3}{2}$

$11= a_{1}+ 15$

$11- 15= a_{1}+ 15 - 15$

$a_{1} = -4$

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Example Question #42 : Sequences And Series

The lengths of the sides of ten squares form an arithmetic sequence. One side of the smallest square measures eight inches; one side of the second-smallest square measures one foot.

Give the area of the largest square.

Possible Answers:

576 square inches

1,936 square inches

484 square inches

784 square inches

2,304 square inches

Correct answer:

1,936 square inches

Explanation:

Let $a_{n}$ be the lengths of the sides of the squares in inches. $a_{1} = 8$ and $a_{2} = 12$ , so their common difference is

$d = a_{2} - a_{1} = 12 - 8 = 4$

The arithmetic sequence formula is

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

The length of a side of the largest square - square 10 - can be found by substituting $a_{1} = 8, n= 10, d = 4$ :

$a_{10} =8+ (10-1) 4 = 8 + 9 \cdot 4 = 8 + 36 = 44$

The largest square has sides of length 44 inches, so its area is the square of this, or $A = 44^{2} = 1,936$ square inches.

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Example Question #11 : Nth Term Of An Arithmetic Sequence

An arithmetic sequence begins as follows:

12, 19, 26, 33,...

Give the thirty-second term of this sequence.

Possible Answers:

229

222

236

250

243

Correct answer:

229

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

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

The initial term in the given sequence is

$a_{1} = 12$ ;

the common difference is

d = 19-12= 7 ;

We are seeking term n = 32 .

This term is

$a_{32} = 12+ (32-1) 7$

$a_{32} = 12+ 31 \cdot 7 = 12+ 217 = 229$

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Example Question #44 : Sequences And Series

An arithmetic sequence begins as follows:

$\frac{2}{5} , \frac{7}{10}, 1, 1 \frac{3}{10}, ...$

Give the thirty-third term of this sequence.

Possible Answers:

$10\frac{1}{10}$

$10 \frac{1}{5}$

$9\frac{4}{5}$

$9\frac{9}{10}$

The correct answer is not given among the other four responses.

Correct answer:

The correct answer is not given among the other four responses.

Explanation:

The th term of an arithmetic sequence with initial term $a_{1}$ and common difference is defined by the equation

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

The initial term in the given sequence is

$a_{1} = \frac{2}{5}$ ;

the common difference is

$d = \frac{7}{10} - \frac{2}{5} = \frac{7}{10} - \frac{4}{10} = \frac{3}{10}$ .

We are seeking term n = 33 .

Therefore,

$a_{33} = \frac{2}{5}+ (33-1) \frac{3}{10}$

$= \frac{2}{5}+ (32) \frac{3}{10}$

$= \frac{2}{5}+ \frac{96}{10}$

$= \frac{2}{5}+ \frac{48}{5}$

$= \frac{50}{5} = 10$ ,

which is not among the choices.

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

What is the value of x in the sequence below?

99, 33, 11, x

Possible Answers:

$3\frac{2}{3}$

$\frac{11}{2}$

$11\frac{1}{3}$

Correct answer:

$3\frac{2}{3}$

Explanation:

In this sequence, each subsequent number is equal to one third of the preceding number.

One third of 11 is equal to:

$\frac{11}{3}=3\frac{2}{3}$

Therefore, the correct answer is: $3\frac{2}{3}$

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

Find the next term of the arithmetic sequence:

24, 29, 34, ?

Possible Answers:

Correct answer:

Explanation:

The common difference for this sequence is . To find the next number in the sequence, add to the last given number.

34+5=39

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Example Question #3 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of this arithmetic sequence:

-15, -8, -1, ?

Possible Answers:

Correct answer:

Explanation:

The common difference for this sequence is . Add this to the last given term to find the next one.

-1+7=6

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

Find the next term of the arithmetic sequence:

-4, 5, 14, ?

Possible Answers:

Correct answer:

Explanation:

The common difference is . Add this to the last given term to find the next term.

14+9=23

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SSAT Upper Level Math : Arithmetic Sequences

Study concepts, example questions & explanations for SSAT Upper Level Math

All SSAT Upper Level Math Resources

Example Questions

Example Question #7 : Nth Term Of An Arithmetic Sequence

Example Question #3 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #10 : How To Find The Nth Term Of An Arithmetic Sequence

Example Question #42 : Sequences And Series

Example Question #11 : Nth Term Of An Arithmetic Sequence

Example Question #44 : Sequences And Series

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

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

All SSAT Upper Level Math Resources

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