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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, ...

2 Answers

2 votes

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\\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.

User Rodrigo Chaves
by
7.8k points
6 votes
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.
User Giaosudau
by
8.9k points

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