Question

Which sequences are arithmetic? Check all that apply. –5, 5, –5, 5, –5, … 96, 48, 24, 12, 6 18, 5.5, –7, –19.5, –32, … –1, –3, –9, –27, –81, … 16, 32, 48, 64, 80

Answer 1

16, 32, 48, 64, 80
18, 5.5, -7, -19.5, -32

Answer 2

18,5.5, –7, –19.5, –32

16, 32, 48, 64, 80.

Explanation:

Arithmetic sequences are a series of numbers of which the difference between consecutive numbers is a constant.

We can clearly see that –5, 5, –5, 5, –5, … is not an arithmetic sequence.

96, 48, 24, 12, 6 This is also not an arithmetic sequence. This is a geometric sequence.

Let's take 18,5.5, –7, –19.5, –32

Difference between 1st number and 2nd number:

`18-5.5=12.5`

Difference between 2nd number and 3rd number:

`5.5-(-7)=12.5`

Difference between 3rd number and 4th number:

`-7-(-19.5)=12.5`

Difference between 4th number and 5th number:

`-19.5-(-32)=12.5`

So difference between all the consecutive numbers is a constant. So this is an arithmetic sequence.

–1, –3, –9, –27, –81 this is not an arithmetic sequence. It is a geometric series where every number is multiplied by a constant number.

Let's check this sequence of numbers 16, 32, 48, 64, 80.

Difference between 1st number and 2nd number:

`32-16=16`

Difference between 2nd number and 3rd number:

`48-16=16`

Difference between 3rd number and 4th number:

`64-48=16`

It is clear that these numbers have a common difference. So this is an arithmetic sequence.