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Chapter 5: Problem 102

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(15,30,60,120, \ldots\)

Short Answer

Expert verified
The sequence is geometric with a common ratio \(2\). And the next two terms are \(240\) and \(480\).

Step by step solution

01

Identify Sequence Type

Review the terms in the sequence - \(15,30,60,120 \ldots\) . Check if each term after the first is found by adding/subtracting or multiplying/dividing a certain number. Here, each term is twice the preceding term, suggesting it's a geometric sequence, i.e., \(30梅15 = 2\), \(60梅30 = 2\), \(120梅60 = 2\). The fact that the ratio between every two successive terms is the same confirms a geometric sequence.
02

Determine the Common Ratio

The common ratio in a geometric sequence is the factor we multiply (or divide) each term by to get the next term. Here, the common ratio can be confirmed as \(2\). This is because every term is doubled or multiplied by \(2\).
03

Determine the next two terms

Using the identified common ratio, compute the next two terms of the sequence. Multiply the last term given in the sequence by the common ratio to find the succeeding terms: \(120*2 = 240\) and then \(240*2 = 480\).

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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, \(r\). \(a_{1}=2000, r=-1\)

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=-2, r=-3\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(\frac{2}{3}, 1, \frac{4}{3}, \frac{5}{3}, \ldots\)

Determine whether each sequence is arithmetic or geometric. Then find the next two terms. \(3,8,13,18, \ldots\)

What is an arithmetic sequence? Give an example with your description.
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