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Sequences and means

(See attached file for full problem description)

1. Find the sum of the finite geometric series to three decimal places.

9 n
Σ - 3(0.5)
n=3

2. Write the first 5 terms of the specified sequence. Determine whether the sequence is arithmetic. If it is, find the common difference.
Problem is "a(sub n)" = "1 over n+3"
a = _1_
n n+3

3. Find the sum of the first 14 terms of the arithmetic sequence, if the first term is -4 and the common difference is 5.

4. Find three arithmetic means between -5 and -37.

5. Determine which of the four sequences below are geometric.
7,14,28,56,112,...
7,1,-5,-11,-17,...
7,8,9,11,12,...
7,-14,28,-56,112,...

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Solution Preview

Please see the attached file.

1. Find the sum of the finite geometric series to three decimal places.

9 n
Σ - 3(0.5)
n=3

By a formula , we have

9 n
Σ - 3(0.5)
n=3
= .............Take out a factor (-3)
= ........... Take out a factor (0.5)^3

.............Apply the formula with r=0.5 and n=6

2. Write the first 5 terms of the specified sequence. Determine whether the sequence is arithmetic. If it is, find the common difference.
...

Solution Summary

The problems in this set include geometric and arithmetic sequences and means. Which of the sequences are geometric are determined.

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