Questions

Math Transition To College Math - Unit 17: Sequences and Series

1) Define a sequence.

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2) Explain the difference between an infinite sequence and a finite sequence.

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3) Define an explicit formula.

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For the next five problems write the first four terms of each sequence defined by the given explicit formula. (Refer to Example #2 in the topic “Sequence”.)

4) Write the first four terms of the sequence.

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5) Write the first four terms of the sequence.

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6) Write the first four terms of the sequence.

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7) Write the first four terms of the sequence.

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8) Write the first four terms of the sequence.

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9) Define a recursive formula.

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For the next four problems, write the first five terms of each sequence defined by the given recursive formula. (Refer to Example #3 in the topic “Sequence”.)

10) Write the first five terms of the sequence.

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11) Write the first five terms of the sequence.

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12) Write the first five terms of the sequence.

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13) Write the first five terms of the sequence.

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14) Define a series.

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For the next four problems, write the terms of each series, and then evaluate. (Refer to Example #2 in the topic “Series”.)

15) Write the terms of the series, and then evaluate.

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16) Write the terms of the series, and then evaluate.

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17) Write the terms of the series, and then evaluate.

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18) Write the terms of the series, and then evaluate.

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19) Define an arithmetic sequence.

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For the next three problems, find the indicated term of the sequence defined by the given recursive formula. (Refer to Example #1 in the topic “Arithmetic Sequences.)

20) Find the third term of the sequence defined by the recursive formula:

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21) Find the fourth term of the sequence defined by the recursive formula:

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22) Find the fifth term of the sequence defined by the recursive formula:

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23) Define an arithmetic series.

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For each arithmetic series in the next three problems, find the indicated sum shown below. (Refer to Example #1 in the topic “Arithmetic Series”.)

24) 3 + 7 + 11 + 15 + …

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25) (-12) + (-6) + 0 + 6 + …

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26) (-17) + (-12) + (-7) + (-2) + 3 + …

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For the next four problems, evaluate each summation, (Refer to Example #2 in the topic “Arithmetic Series”.)

27) Evaluate the summation.

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28) Evaluate the summation.

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29) Evaluate the summation.

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30) Evaluate the summation.

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31) Define a geometric sequence.

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For the next three problems, find the sixth term in the geometric sequence that includes each pair of terms indicated. (Refer to Example #2 in the topic “Geometric Sequences”.)

32) Find the sixth term in the geometric sequence.

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33) Find the sixth term in the geometric sequence.

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34) Find the sixth term in the geometric sequence.

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35) Define a geometric series.

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For the next three problems, evaluate. (Refer to Example #2 in the topic “Geometric Series”.)

36) Evaluate.

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37) Evaluate.

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38) Evaluate.

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