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SSAT Upper Level Math : nth Term of an Arithmetic Sequence

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Example Questions

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

Find the next term of the arithmetic sequence:

$-\frac{1}{2}, 3, \frac{13}{2}, ?$

Possible Answers:

$\frac{19}{2}$

$\frac{17}{2}$

Correct answer:

Explanation:

The common difference is $\frac{7}{2}$ . Add this to the last given term to find the next term.

$\frac{13}{2}+\frac{7}{2}=\frac{20}{2}=10$

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

Find the next term of the arithmetic sequence:

5, -2, -9, ?

Possible Answers:

Correct answer:

Explanation:

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

-9+(-7)=-16

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Example Question #7 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of the arithmetic sequence:

-14, -8, -2, ?

Possible Answers:

Correct answer:

Explanation:

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

-2+6=4

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SSAT Upper Level Math : nth Term of an Arithmetic Sequence

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

All SSAT Upper Level Math Resources

Example Questions

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

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

All SSAT Upper Level Math Resources

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