Question

determine if the sequence below is arithmetic or geometric and determine the common difference / ratio in simplest form.

1, 9, 81, ...

answer
attempt 1 out of 2

this is sequence
and the is
equal to .

Explanation:

Step1: Check arithmetic sequence

Calculate differences: $9-1=8$, $81-9=72$. Since $8
eq 72$, it is not arithmetic.

Step2: Check geometric sequence

Calculate ratios: $\frac{9}{1}=9$, $\frac{81}{9}=9$. Since ratios are equal, it is geometric.

Answer:

This is a geometric sequence and the common ratio is equal to 9.