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Arithmetic Sequence Differences

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Use the arithmetic sequence of numbers 1, 3, 5, 7, 9, ..... to find the following:

a. What is d, the difference between any 2 terms

b. Using the formula for the nth term of an arithmetic sequence, what is 101st term?

c. Using the formula for the sum of an arithmetic series, what is the sum of the first 20 term?

d. Using the formula for the sum of an arithmetic series, what is the sum of the first 30 term?

e. What observation can you make about these sums of this series (Hint: It would be beneficial to find a few more sums like the sum of the first 2, then the first 3, )?

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Solution Summary

The solution shows the formula for the sums of arithmetic series for different amounts of terms.

Solution Preview

a.
Sequence 1, 3, 5, 7, 9, ..... => a(n) = 2*n-1

d = ...

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