Question

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

Answer 1

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 != a_2-a_1`, so the sequence is not arithmetic.

Geometric sequence

`40/80=20/40=10/20=5/10=0.5`

The quotient of 2 consecutive terms is constant `1/2`, so the sequence is geometric.

Answer 2

No.. its not

Explanation:

The sequence `80,40,20,10,5,...` is formed by division i.e. `80/2 = 40, 40/2 = 20, 20/2 = 10....`

And, their common ratio is `2`, as `80/40=2, 40/20=2, 20/10=2....`

Therefore this sequence is geometric .

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