Question

Is 1/3, 2/3, 4/3, 8/3, 16/3 arithmetic sequence

Answer 1

The given sequence is not arithmetic sequence

Solution:

Given sequence is:

$\frac{1}{3} , \frac{2}{3} , \frac{4}{3} , \frac{8}{3} , \frac{16}{3}$

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

$\text{ first term } = a_1 = \frac{1}{3}\\\\\text{ second term } = a_2 = \frac{2}{3}\\\\\text{ third term } = a_3 = \frac{4}{3}\\\\\text{ fourth term } = a_4 = \frac{8}{3}\\\\\text{ fifth term } = a_5 = \frac{16}{3}$

Let us find the difference between terms

$a_2 - a_1 = \frac{2}{3} - \frac{1}{3} = \frac{1}{3}$

$a_3 - a_2 = \frac{4}{3} - \frac{2}{3} = \frac{2}{3}$

$a_4 - a_3 = \frac{8}{3} - \frac{4}{3} = \frac{4}{3}$

$a_5 - a_4 = \frac{16}{3} - \frac{8}{3} = \frac{8}{3}$

Thus the difference between terms is not constant

So the given sequence is not arithmetic sequence