Question

Which of the following sequences is arithmetic?

0, 3, 6, 9, 12, ...
1, 4, 9, 16, 25, ...
200, 100, 50, 25, ...
4, 12, 36, 108, ...

Answer 1

Option A is the answer.

Step-by-step explanation:

If a sequence is given in the form of
`a_(1), a_(2), a_(3)........a_(n-1), a_(n)`

Then the given sequence will be an arithmetic sequence if

`a_(2)-a_(1)=a_(3)-ax_(2)=a_(n)-a_(n-1)=d`

Here d represents common difference.

Now we will check each option given in the question.

Option A.

0, 3, 6, 9, 12.....

As per definition
`d=3-0=6-3=9-6=3`

Therefore this sequence is an arithmetic sequence.

Option B.

1, 4, 9, 16, 25.......

`4-1\\eq 9-4\\eq 16-9`

Since difference between the terms is not common so the sequence is not an arithmetic sequence.

Option C.

200, 100, 50, 25.......

`100-200\\eq 100-50\\eq 50-25`

Since difference is not common in each term so it's not an arithmetic sequence.

Option D.

4, 12, 36, 108..........

Now common difference

`12-4\\eq 36-12\\eq 108-36`

So this sequence is not an arithmetic sequence.

Answer is Option A.

Answer 2

Answer:
0, 3, 6, 9, 12 .....

Step-by-step explanation:
An arithmetic sequence is defined as a sequence of numbers that increases or decreases by a constant value.
The values are increasing when the same number is added or subtracted onto the number.
The rest of the choices do not have a constant number being added or subtracted they are either:
multiplied: option (D),
divided: option (C),
a list of perfect squares: option (B).

The answer (A) had the constant of 3 added to each term increasing forever.