Question

Which of the following is an arithmetic sequence?–20, –25, –30, –35, –45, ...

–15.6, –12.9, –10.2, –7.5, –4.8, ...

3.1, 6.2, 12.4, 24.8, 49.6, ...

7.2, 3.6, 1.8, 0.9, 0.45, ...

Answer 1

B) -15.6,-12.9,-10.2,-7.5,-4.8

This is an arithmetic sequence.

Answer 2

The correct option is 2.

Explanation:

A sequence is called arithmetic if it has common difference.

In sequence 1,

–20, –25, –30, –35, –45, ...

`d_1=-25-(-20)=-5`

`d_2=-45-(-35)=-10`

`d_1\\eq d_2`

Therefore it is not an arithmetic sequence.

In sequence 2, the common difference is

`d=-12.9-(-15.6)=2.7`

Therefore it is an arithmetic sequence and option 2 is correct.

In sequence 3,

`d_1=6.2-3.1=3.1`

`d_2=12.4-6.2=6.2`

`d_1\\eq d_2`

Therefore it is not an arithmetic sequence.

In sequence 4,

`d_1=3.6-7.2=-3.6`

`d_2=1.8-3.6=-1.8`

`d_1\\eq d_2`

Therefore it is not an arithmetic sequence.

Therefore only option 2 represent arithmetic sequence.