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Chapter 5: Problem 103

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(-7,-2,3,8, \ldots\)

Short Answer

Expert verified
The sequence is arithmetic and the next two terms are 13 and 18.

Step by step solution

01

Check for Arithmetic Sequence

First, find the difference between consecutive terms in the sequence. Take the second term (-2) and subtract the first term (-7). So, -2 - (-7) = 5. To see if this a pattern, calculate the difference of the next consecutive terms, 3 - (-2) = 5 and 8 - 3 = 5. As all differences are equal, it confirms that the sequence is arithmetic.
02

Find the Next Terms of Arithmetic Sequence

For an arithmetic sequence, the next term can be calculated by adding the common difference to the previous term. Here, the common difference is 5, so add 5 to the last given term 8. Thus, the next term is 8 + 5 = 13. And the term after that is 13 + 5 = 18.
03

Check for Geometric Sequence

Checking for a geometric sequence in this context is unnecessary because the sequence has already been determined as arithmetic. However, in doing so for educational purposes, one would divide each term by its predecessor to see if the quotient was constant. This is not the case for the given sequence.

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Most popular questions from this chapter

Enough curiosities involving the Fibonacci sequence exist to warrant a flourishing Fibonacci Association. It publishes a quarterly journal. Do some research on the Fibonacci sequence by consulting the research department of your library or the Internet, and find one property that interests you. After doing this research, get together with your group to share these intriguing properties.

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 geometric sequence. Then use the formula for \(a_{n}\) to find \(a_{7}\), the seventh term of the sequence. \(12,6,3, \frac{3}{2}, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(7,-7,-21,-35, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(6,-6,-18,-30, \ldots\)
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