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Chapter 5: Problem 100

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

Short Answer

Expert verified
The sequence is arithmetic with a common difference of 5. The next two terms in the sequence are 23 and 28.

Step by step solution

01

Identify the Type of Sequence

To identify whether the sequence is arithmetic or geometric, examine the difference or ratio between terms. The sequence provided is \(3, 8, 13, 18\). The difference from one term to the next is consistent; \(8 - 3 = 5\), \(13 - 8 = 5\), and \(18 - 13 = 5\). Hence, this is an arithmetic sequence because there is a common difference of 5.
02

Determine the Next Two Terms

Once the common difference is identified, this value can be added to the last given term to get the next terms. Start from the last known term, which is 18, and add the common difference which is 5. This gives us \(18 + 5 = 23\). Repeat this with the number just calculated, resulting in \(23 + 5 = 28\). So, the next two terms of the sequence are 23 and 28.

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Most popular questions from this chapter

What is a geometric sequence? Give an example with your description.

Find the indicated term for the geometric sequence with first term, \(a_{1}\), and common ratio, \(r\). Find \(a_{40}\), when \(a_{1}=6, r=-1\).

Write the first six terms of the geometric sequence with the first term, \(a_{1}\), and common ratio, \(r\). \(a_{1}=\frac{1}{4}, r=2\)

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. \(18,6,2, \frac{2}{3}, \ldots\)

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