The given sequence is not arithmetic sequence
Solution:
Given sequence is:
[tex]\frac{1}{3} , \frac{2}{3} , \frac{4}{3} , \frac{8}{3} , \frac{16}{3}[/tex]
We have to find if the above sequence is arithmetic sequence or not
An arithmetic sequence is a sequence of numbers such that the difference of any two successive members of the sequence is a constant
Here in the given sequence
[tex]\text{ first term } = a_1 = \frac{1}{3}\\\\\text{ second term } = a_2 = \frac{2}{3}\\\\\text{ third term } = a_3 = \frac{4}{3}\\\\\text{ fourth term } = a_4 = \frac{8}{3}\\\\\text{ fifth term } = a_5 = \frac{16}{3}[/tex]
Let us find the difference between terms
[tex]a_2 - a_1 = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}[/tex]
[tex]a_3 - a_2 = \frac{4}{3} - \frac{2}{3} = \frac{2}{3}[/tex]
[tex]a_4 - a_3 = \frac{8}{3} - \frac{4}{3} = \frac{4}{3}[/tex]
[tex]a_5 - a_4 = \frac{16}{3} - \frac{8}{3} = \frac{8}{3}[/tex]
Thus the difference between terms is not constant
So the given sequence is not arithmetic sequence
