Question

Which of the following sequences is arithmetic?

Answer 1

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

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.

Answer 2

Answer:

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.......

$4-1\neq 9-4\neq 16-9$

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

Option C.

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

$100-200\neq 100-50\neq 50-25$

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

Option D.

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

Now common difference

$12-4\neq 36-12\neq 108-36$

So this sequence is not an arithmetic sequence.

Answer is Option A.