How do you tell whether the sequence -8, 24, -72.... is arithmetic, geometric, or neither?

Oct 22, 2015

The sequence is a geometric sequence.

Explanation:

$- 8 , 24 , - 72. . .$

• Checking if it a geometric sequence :

In a geometric sequence a common ratio $r$ is constantly maintained between any two consecutive terms.

$r$ is obtained by dividing a term by its preceding term

${r}_{1} = \frac{24}{-} 8 = - 3$

${r}_{2} = - \frac{72}{24} = - 3$

Since ${r}_{1} = {r}_{2}$ this shows that the ratio maintained is constant, so the sequence is geometric in nature.

• Checking if the sequence is an arithmetic progression:

For an arithmetic progression a common difference $d$ is maintained between two consecutive terms.

${d}_{1} = 24 - \left(- 8\right) = 24 + 8 = 32$

${d}_{2} = - 72 - 24 = - 96$

Since ${d}_{1} \ne {d}_{2}$ the sequence is not an arithmetic sequence.