SSAT Upper Level Math : How to find the next term in an arithmetic sequence

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

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Example Questions

Example Question #542 : Number Concepts And Operations

What is the value of x in the sequence below?

\displaystyle 99, 33, 11, x

Possible Answers:

\displaystyle 4

\displaystyle 11\frac{1}{3}

\displaystyle 3\frac{2}{3}

\displaystyle \frac{11}{2}

Correct answer:

\displaystyle 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:

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

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

Example Question #52 : Sequences And Series

Find the next term of the arithmetic sequence:

 

\displaystyle 24, 29, 34, ?

Possible Answers:

\displaystyle 38

\displaystyle 36

\displaystyle 39

\displaystyle 30

Correct answer:

\displaystyle 39

Explanation:

The common difference for this sequence is \displaystyle 5. To find the next number in the sequence, add \displaystyle 5 to the last given number.

\displaystyle 34+5=39

Example Question #53 : Sequences And Series

Find the next term of this arithmetic sequence:

\displaystyle -15, -8, -1, ?

Possible Answers:

\displaystyle 5

\displaystyle 7

\displaystyle 6

\displaystyle 4

\displaystyle 3

Correct answer:

\displaystyle 6

Explanation:

The common difference for this sequence is \displaystyle 7. Add this to the last given term to find the next one.

\displaystyle -1+7=6

Example Question #54 : Sequences And Series

Find the next term of the arithmetic sequence:

\displaystyle -4, 5, 14, ?

Possible Answers:

\displaystyle 24

\displaystyle 20

\displaystyle 22

\displaystyle 23

Correct answer:

\displaystyle 23

Explanation:

The common difference is \displaystyle 9. Add this to the last given term to find the next term.

\displaystyle 14+9=23

Example Question #55 : Sequences And Series

Find the next term of the arithmetic sequence:

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

Possible Answers:

\displaystyle \frac{17}{2}

\displaystyle 11

\displaystyle 10

\displaystyle \frac{19}{2}

Correct answer:

\displaystyle 10

Explanation:

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

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

Example Question #56 : Sequences And Series

Find the next term of the arithmetic sequence:

\displaystyle 5, -2, -9, ?

Possible Answers:

\displaystyle -20

\displaystyle -15

\displaystyle -16

\displaystyle -17

Correct answer:

\displaystyle -16

Explanation:

The common difference is \displaystyle -7. Add this to the last given term to find the next term.

\displaystyle -9+(-7)=-16

Example Question #57 : Sequences And Series

Find the next term of the arithmetic sequence:

\displaystyle -14, -8, -2, ?

Possible Answers:

\displaystyle 2

\displaystyle 4

\displaystyle 6

\displaystyle 3

Correct answer:

\displaystyle 4

Explanation:

The common difference is \displaystyle 6. Add this to the last given term to find the next term.

\displaystyle -2+6=4

Example Question #551 : Number Concepts And Operations

Find the next term of the arithmetic sequence:

\displaystyle -15, 11, 37, ?

Possible Answers:

\displaystyle 73

\displaystyle 63

\displaystyle 62

\displaystyle 26

Correct answer:

\displaystyle 63

Explanation:

The common difference is \displaystyle 26. Add this to the last given term to find the next term.

\displaystyle 37+26=63

Example Question #552 : Number Concepts And Operations

Find the next term of the arithmetic sequence:

\displaystyle 10, 130, 250, ?

Possible Answers:

\displaystyle 350

\displaystyle 300

\displaystyle 370

\displaystyle 470

Correct answer:

\displaystyle 370

Explanation:

The common difference is \displaystyle 120. Add this to the last given term to find the next term.

\displaystyle 250+120=370

Example Question #553 : Number Concepts And Operations

Find the next term in the following arithmetic sequence:

\displaystyle \frac{9}{2}, 4, \frac{7}{2}, ?

Possible Answers:

\displaystyle \frac{5}{2}

\displaystyle \frac{3}{2}

\displaystyle 3

\displaystyle 2

Correct answer:

\displaystyle 3

Explanation:

The common difference for this arithmetic sequence is \displaystyle -\frac{1}{2}. To find the next term in the sequence, subtract that value from the last given value.

\displaystyle \frac{7}{2}-\frac{1}{2}=3

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