Chapter 3.6, Problem 16PPS

To determine

To Find: The next three terms of the arithmetic sequence $2\frac{1}{3},2\frac{2}{3},3,3\frac{1}{3},\mathrm{............}$

Answer to Problem 16PPS

The next three terms of the sequence are $3\frac{2}{3},4\&4\frac{1}{3}$ .

Explanation of Solution

Given information:

Arithmetic sequence $2\frac{1}{3},2\frac{2}{3},3,3\frac{1}{3},\mathrm{............}$

Concept and Formula Used:

Arithmetic Sequence: The sequence with difference between successive terms is constant.

Calculation:

It is given that arithmetic sequence is $2\frac{1}{3},2\frac{2}{3},3,3\frac{1}{3},\mathrm{............}$

The common difference between terms is $d=2\frac{2}{3}-2\frac{1}{3}=3-2\frac{2}{3}=3\frac{1}{3}-3=\frac{1}{3}$

To find next three terms add $\frac{1}{3}$ to the last term of the sequence to get the next term.

The next three terms are

  $\begin{array}{l}3\frac{1}{3}+\left(\frac{1}{3}\right)=3\frac{2}{3}\\ 3\frac{2}{3}+\left(\frac{1}{3}\right)=4\\ 4+\left(\frac{1}{3}\right)=4\frac{1}{3}\end{array}$

Conclusion:

The next three terms of the sequence are $3\frac{2}{3},4\&4\frac{1}{3}$ .