# How do you determine whether the sequence 80, 40, 20, 10, 5,... is arithmetic and if it is, what is the common difference?

Oct 9, 2017

See explanation.

#### Explanation:

To find if a sequence is arithmwtic, geometric or neither you have to check if either the difference (arithmetic sequence) or quotient (geometric sequence) between any 2 consecutive terms is constant.

Arithmetic sequence

${a}_{1} = 80$, ${a}_{2} = 40$, ${a}_{3} = 20$

${a}_{2} - {a}_{1} = 40 - 80 = - 40$

${a}_{3} - {a}_{2} = 20 - 40 = - 20$

${a}_{3} - {a}_{2} \ne {a}_{2} - {a}_{1}$, so the sequence is not arithmetic.

Geometric sequence

$\frac{40}{80} = \frac{20}{40} = \frac{10}{20} = \frac{5}{10} = 0.5$

The quotient of 2 consecutive terms is constant $\frac{1}{2}$, so the sequence is geometric.

Oct 9, 2017

No.. its not

#### Explanation:

The sequence $80 , 40 , 20 , 10 , 5 , \ldots$ is formed by division i.e. $\frac{80}{2} = 40 , \frac{40}{2} = 20 , \frac{20}{2} = 10. \ldots$

And, their common ratio is $2$, as $\frac{80}{40} = 2 , \frac{40}{20} = 2 , \frac{20}{10} = 2. \ldots$

Therefore this sequence is geometric .

It would be arithmetic if the next term was formed by addition or subtraction.