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

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Example Questions

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

What is the value of x in the sequence below?

$\displaystyle 99, 33, 11, x$

Possible Answers:

$11\frac{1}{3}$ $\displaystyle 11\frac{1}{3}$

$3\frac{2}{3}$ $\displaystyle 3\frac{2}{3}$

$\displaystyle 4$

$\frac{11}{2}$ $\displaystyle \frac{11}{2}$

Correct answer:

$3\frac{2}{3}$ $\displaystyle 3\frac{2}{3}$

Explanation:

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

One third of 11 is equal to:

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

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

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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:

$\displaystyle 24, 29, 34, ?$

Possible Answers:

$\displaystyle 36$

$\displaystyle 39$

$\displaystyle 38$

$\displaystyle 30$

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.

34+5=39 $\displaystyle 34+5=39$

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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:

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

Possible Answers:

$\displaystyle 5$

$\displaystyle 3$

$\displaystyle 6$

$\displaystyle 4$

$\displaystyle 7$

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.

-1+7=6 $\displaystyle -1+7=6$

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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:

$\displaystyle -4, 5, 14, ?$

Possible Answers:

$\displaystyle 20$

$\displaystyle 22$

$\displaystyle 24$

$\displaystyle 23$

Correct answer:

$\displaystyle 23$

Explanation:

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

14+9=23 $\displaystyle 14+9=23$

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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:

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

Possible Answers:

$\displaystyle 10$

$\displaystyle 11$

$\frac{19}{2}$ $\displaystyle \frac{19}{2}$

$\frac{17}{2}$ $\displaystyle \frac{17}{2}$

Correct answer:

$\displaystyle 10$

Explanation:

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

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

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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:

$\displaystyle 5, -2, -9, ?$

Possible Answers:

$\displaystyle -16$

$\displaystyle -20$

$\displaystyle -15$

$\displaystyle -17$

Correct answer:

$\displaystyle -16$

Explanation:

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

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

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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:

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

Possible Answers:

$\displaystyle 4$

$\displaystyle 2$

$\displaystyle 6$

$\displaystyle 3$

Correct answer:

$\displaystyle 4$

Explanation:

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

-2+6=4 $\displaystyle -2+6=4$

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Example Question #8 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of the arithmetic sequence:

$\displaystyle -15, 11, 37, ?$

Possible Answers:

$\displaystyle 62$

$\displaystyle 73$

$\displaystyle 26$

$\displaystyle 63$

Correct answer:

$\displaystyle 63$

Explanation:

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

$\displaystyle 37+26=63$

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Example Question #9 : How To Find The Next Term In An Arithmetic Sequence

Find the next term of the arithmetic sequence:

$\displaystyle 10, 130, 250, ?$

Possible Answers:

300 $\displaystyle 300$

350 $\displaystyle 350$

370 $\displaystyle 370$

470 $\displaystyle 470$

Correct answer:

370 $\displaystyle 370$

Explanation:

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

$\displaystyle 250+120=370$

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Example Question #10 : How To Find The Next Term In An Arithmetic Sequence

Find the next term in the following arithmetic sequence:

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

Possible Answers:

$\frac{3}{2}$ $\displaystyle \frac{3}{2}$

$\frac{5}{2}$ $\displaystyle \frac{5}{2}$

$\displaystyle 3$

$\displaystyle 2$

Correct answer:

$\displaystyle 3$

Explanation:

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

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

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All SSAT Upper Level Math Resources

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

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

All SSAT Upper Level Math Resources

Example Questions

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

Example Question #8 : How To Find The Next Term In An Arithmetic Sequence

Example Question #9 : How To Find The Next Term In An Arithmetic Sequence

Example Question #10 : How To Find The Next Term In An Arithmetic Sequence

All SSAT Upper Level Math Resources

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