Question

Find the next four terms of each arithmetic sequence.

$\frac{1}{3},1,\frac{5}{3},\mathrm{...}$

Short answer

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$\frac{1}{3},1,\frac{5}{3},\mathrm{...}$

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 $\frac{7}{3},3,\frac{11}{3},\frac{13}{3}$.