Question

Which answer describes the type of sequence?

1/6, 1/2, 3/2, 9/2, ...


neither arithmetic nor geometric

geometric

arithmetic

Answer 1

Answer:

The sequence is a geometric sequence.

Step-by-step explanation:

The given sequence is

$\frac{1}{6},\frac{1}{2},\frac{3}{2},\frac{9}{2},...$

We examine to see whether there is a common difference or a common ratio.

We first check for a common difference by subtracting the subsequent terms.

$\frac{1}{2}-\frac{1}{6}=\frac{2}{3}$

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

The two differences are not equal.

Hence the sequence is not arithmetic.

We now look out for a common ratio.

$\frac{1}{2}\div \frac{1}{6}=3$

$\frac{3}{2}\div \frac{1}{2}=3$

$\frac{9}{2}\div \frac{3}{2}=3$

Since there is a common ratio of 3, the sequence is geometric.