# Sequences and means

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(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 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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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.

...

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

###### Recent Feedback

- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"

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