The sequence 0, 3, 6, 9, 12, . . . is an arithmetic sequence.
What is sequence?
"It is an arrangement of a set of numbers in a particular order."
What is an arithmetic sequence?
"It is a sequence where the differences between every two consecutive terms is the same."
For given example,
We have been given a four sequences.
We need to find which sequence is arithmetic sequence.
First we find the difference between two consecutive terms for each sequence and then conclude which sequence is arithmetic sequence.
1) Consider sequence 0, 3, 6, 9, 12, . . .
The difference between two consecutive terms would be,
⇒ 3 - 0 = 3
⇒ 6 - 3 = 3
⇒ 9 - 6 = 3
⇒ 12 - 9 = 3
Since the difference between two consecutive terms is same, the sequence 0, 3, 6, 9, 12, . . . is an arithmetic sequence.
2) Consider sequence 1, 4, 9, 16, 25, . . .
The difference between two consecutive terms would be,
⇒ 4 - 1 = 3
⇒ 9 - 4 = 5
⇒ 16 - 9 = 7
Since the difference between two consecutive terms is not same, the sequence 1, 4, 9, 16, 25, . . . is not a arithmetic sequence.
3) Consider sequence 200, 100, 50, 25, . . .
The difference between two consecutive terms would be,
⇒ 100 - 200 = -100
⇒ 50 - 100 = -50
⇒ 25 - 50 = -25
Since the difference between two consecutive terms is different, the sequence 200, 100, 50, 25, . . . is not a arithmetic sequence.
4) Consider sequence 4, 12, 36, 108, . . .
The difference between two consecutive terms would be,
⇒ 12 - 4 = 8
⇒ 36 - 12 = 24
⇒ 108 - 36 = 72
Since the difference between two consecutive terms is not same, the sequence 4, 12, 36, 108, . . . is not a arithmetic sequence.
Therefore, the sequence 0, 3, 6, 9, 12, . . . is an arithmetic sequence.
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