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

Answer:

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

Answer:

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.