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Chapter 5: Problem 101

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(5,15,45,135, \ldots\)

Short Answer

Expert verified
The sequence is geometric with a common ratio of 3. The next two terms are 405 and 1215.

Step by step solution

01

Determine the sequence type

First, look at the differences or ratios between each pair of terms: \(15 - 5 = 10\), \(45 - 15 = 30\), and \(135 - 45 = 90\). The differences aren't the same, so it's not an arithmetic sequence. Now look at the ratios: \(\frac{15}{5} = 3\), \(\frac{45}{15} = 3\), and \(\frac{135}{45} = 3\). The ratios are the same, so it's a geometric sequence. The common ratio is 3.
02

Find the next terms

Now find the next two terms by multiplying the last term given (135) by the common ratio (3). This gives \(135 \times 3 = 405\), which is the next term. For the term after that, multiply 405 by 3 again to get \(405 \times 3 = 1215\).

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Most popular questions from this chapter

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{8}\), when \(a_{1}=6, r=\frac{1}{2}\).

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