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

2 Answers
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 != 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.

Oct 9, 2017

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.