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Chapter 5: Problem 61

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-6, r=-5\)

Short Answer

Expert verified
The first six terms of the geometric sequence are: -6, 30, -150, 750, -3750, 18750.

Step by step solution

01

Identify the first term and the common ratio

In this geometric sequence, the first term \(a_{1}\) is -6 and the common ratio \(r\) is -5. This information is given in the problem.
02

Calculate the second term

To find the second term of the sequence, we multiply the first term by the common ratio: \(a_{2} = a_{1} \cdot r = -6 \cdot -5 = 30\)
03

Continue the pattern to find the next terms

We continue this pattern to find the next terms: \(a_{3} = a_{2} \cdot r = 30 \cdot -5 = -150\), \(a_{4} = a_{3} \cdot r = -150 \cdot -5 = 750\), \(a_{5} = a_{4} \cdot r = 750 \cdot -5 = -3750\), \(a_{6} = a_{5} \cdot r = -3750 \cdot -5 = 18750\)

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Most popular questions from this chapter

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-1000, r=0.1\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\sqrt{3}, 3,3 \sqrt{3}, 9, \ldots\)

The bar graph shows changes in the percentage of college graduates for Americans ages 25 and older from 1990 to 2010. Exercises 125-126 involve developing arithmetic sequences that model the data. In \(1990,18.4 \%\) of American women ages 25 and older had graduated from college. On average, this percentage has increased by approximately \(0.6\) each year. a. Write a formula for the \(n\)th term of the arithmetic sequence that models the percentage of American women ages 25 and older who had graduated from college \(n\) years after \(1989 .\) b. Use the model from part (a) to project the percentage of American women ages 25 and older who will be college graduates by \(2019 .\)

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. A sequence that is not arithmetic must be geometric.

Write a formula for the general term (the nth term) of each arithmetic sequence. Then use the formula for \(a_{n}\) to find \(a_{20}\), the 20 th term of the sequence. \(2,7,12,17, \ldots\)
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