# Video: Identifying Whether a Given Sequence Is Finite of Infinite

Is the sequence (−9, −6, −3, 0, ..., 21) finite or infinite?

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### Video Transcript

Is the sequence negative nine, negative six, negative three, zero, dot dot dot, 21 finite or infinite?

If a sequence is finite, that means it ends. If a sequence is infinite, it does not end. It goes on forever. So here we have our sequence. And the number of terms in a sequence can be found by considering the relation for the sequence. So how are these terms related? Well, to go from negative nine to negative six, we must add three. To go from negative six to negative three, we must add three. To go from negative three to zero, we must add three.

So we can actually fill in the rest of the sequence by adding three every time. So if we would add three to zero, we would get three. If we would add three to three, we would get six. If we would add three to six, we would get nine. If we would add three to nine, we would get 12. If we would add three to 12, we would get 15. And if we would add three to 15, we would get 18. And lastly, if we would add three to 18, we would get 21, which is exactly what we were supposed to end with.

And notice, we just said the word end. This sequence ends at the number 21. So it must be finite. And if a sequence is finite, it will have a specific number of terms. Let’s count, one, two, three, four, five, six, seven, eight, nine, 10, 11. And since there are 11 terms, this is a finite number. Therefore, this sequence is finite.