Chapter 11: Q19. (page 581)

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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Find the next four terms of each arithmetic sequence.13,1,53,...

Short Answer

Step by step solution

Step 1. Given Information.

Step 2. Calculation.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

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