Question

Which set of numbers is an arithmetic sequence?1, 5, 8, 13, ...2, 4, 8, 32, ...25, 21, 17, 13, ...81, 27, 9, 3, ...

Answer 1

That would be 25,21,17,13...

this is arithmetic with a common difference of -4.

Answer 2

The correct option is 3.

Explanation:

The sequence is called an arithmetic sequence if the difference between every two consecutive terms are same.

In sequence 1, 5, 8, 13, ...

`d_1=a_2-a_1=5-1=4`

`d_2=a_3-a_2=8-5=3`

Since
`d_1\\eq d_2`, therefore the sequence 1, 5, 8, 13, ... is not an arithmetic sequence.

In sequence 2, 4, 8, 32,...

`d_1=a_2-a_1=4-2=2`

`d_2=a_3-a_2=8-4=4`

Since
`d_1\\eq d_2`, therefore the sequence 2, 4, 8, 32,... is not an arithmetic sequence.

In sequence 25, 21, 17, 13, ...

`d_1=a_2-a_1=21-25=-4`

`d_2=a_3-a_2=17-21=-4`

`d_3=a_4-a_3=13-17=-4`

Since this sequence has common difference of -4 therefore the sequence 25, 21, 17, 13, ... is an arithmetic sequence.

In sequence 81, 27, 9, 3, ...

`d_1=a_2-a_1=27-81=-54`

`d_2=a_3-a_2=9-27=-18`

Since
`d_1\\eq d_2`, therefore the sequence 81, 27, 9, 3, ... is not an arithmetic sequence.

Hence the correct option is 3.