Question

Which answer describes the type of sequence? 200, 40, 8, 1.6, ...

-geometric

-arithmetic

-neither arithmetic nor geometric

Answer 1

Option 1 the given sequence is a geometric.

Explanation:

We have been given with the series

`200,40,8,1.6`

Arithmetic sequence is the sequence in which difference between consecutive terms is same that is common difference d

`d=a_2-a_1`

`d=40-200=-160` here
`a_2=40,a_1=200`

`d=8-40=-32` here
`a_2=8,a_1=40`

We can see the difference is not same

Hence, the given sequence is not arithmetic sequence.

Geometric sequence is the sequence in which ratio of consecutive terms is same that is common ratio r

`r=(a_2)/(a_1)`

`r=(40)/(200)=(1)/(5)` here
`a_2=40,a_1=200`

`r=(8)/(40)=(1)/(5)` here
`a_2=8,a_1=40`

`r=(1.6)/(8)=(1)/(5)` here
`a_2=1.6,a_1=8`

We can see the ratio is same.

Hence, given sequence is geometric

Therefore, Option 1 is correct given sequence is geometric.