Chapter 11: Q. 19 (page 586)

Find the next four terms of each arithmetic sequence.
$\frac{1}{3}, 1, \frac{5}{3}, ...$

Short Answer

Expert verified

The next four terms of the arithmetic sequence are $\frac{7}{3}, 3, \frac{11}{3}, \frac{13}{3}$ .

Step by step solution

Step 1. Given Information.

The given arithmetic sequence is $\frac{1}{3}, 1, \frac{5}{3}, ...$

Step 2. Calculation.

A sequence is said to be arithmetic when the difference between the consecutive terms is always the same.

Here the difference between the first two terms is $1 - \frac{1}{3} = \frac{2}{3}$

The difference between the next two terms is $\frac{5}{3} - 1 = \frac{2}{3}$

So, the common difference is $\frac{2}{3}$

The next term in the arithmetic sequence is $\frac{5}{3} + \frac{2}{3} = \frac{7}{3}$

The next term in the arithmetic sequence is $\frac{7}{3} + \frac{2}{3} = \frac{9}{3} = 3$

The next term in the arithmetic sequence is $3 + \frac{2}{3} = \frac{11}{3}$

The next term in the arithmetic sequence is $\frac{11}{3} + \frac{2}{3} = \frac{13}{3}$

Step 3. Conclusion.

Hence, the next four terms of the arithmetic sequence are $\frac{7}{3}, 3, \frac{11}{3}, \frac{13}{3}$ .

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Find the next four terms of each arithmetic sequence.
$\frac{1}{3}, 1, \frac{5}{3}, ...$

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

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Step by step solution

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Find the next four terms of each arithmetic sequence.
$\frac{1}{3}, 1, \frac{5}{3}, ...$