Question

Is the sequence geometric if so identify the common ratio 1/3, 2/9, 4/27, 8/81, 16/243

Answer 1

Answer:

Yes, the given sequence is geometric and the common ratio is $\frac{2}{3}$.

Step-by-step explanation:

The given sequence is

$\frac{1}{3},\frac{2}{9},\frac{4}{27},\frac{8}{81},\frac{16}{243}$

If the ratio of all two consecutive terms are same, then the sequence is called geometric.

$r=\frac{a_{n+1}}{a_n}$

$r_1=\frac{\frac{2}{9}}{\frac{1}{3}}=\frac{2}{3}$

$r_2=\frac{\frac{4}{27}}{\frac{2}{9}}=\frac{2}{3}$

$r_3=\frac{\frac{8}{81}}{\frac{4}{27}}=\frac{2}{3}$

$r_4=\frac{\frac{16}{243}}{\frac{8}{81}}=\frac{2}{3}$

$r_1=r_2=r_3=r_4$

Therefore the given sequence is geometric and the common ratio is $\frac{2}{3}$.

Answer 2

Yes it is a geometric sequence and the common ratio is 2/3