Math Lesson

FINITE vs INFINITE SEQUENCE

A finite sequence has an end, while an infinite sequence goes on forever without stopping!

A finite sequence stops at a certain term. An infinite sequence never ends and is usually indicated by three dots (...) at the end.

Finite: a₁, a₂, a₃, ..., a_n
Infinite: a₁, a₂, a₃, ..., a_n, ...

What is a Finite Sequence?

A finite sequence is a sequence that has a definite number of terms. It eventually comes to an end.

Example: 2, 4, 6, 8
Notice that there is no continuation. It ends at the number 8. This means it has exactly 4 terms.

What is an Infinite Sequence?

An infinite sequence is a sequence that continues endlessly. It does not have a last term. We use an ellipsis (three dots ...) to show that the sequence goes on forever.

Example: 2, 4, 6, 8, ...
The three dots mean the sequence continues to infinity.

4 Worked Examples

Example 1: Identify if the sequence is finite or infinite.

Sequence: 5, 10, 15, 20

Look at the end. There are no three dots. It ends at 20.

Answer: Finite Sequence

Example 2: Identify if the sequence is finite or infinite.

Sequence: 1, 2, 3, 4, ...

Notice the three dots (...) at the end. This means it continues forever.

Answer: Infinite Sequence

Example 3: How many terms are in the finite sequence?

Sequence: 3, 6, 9, 12, 15

Count the terms individually:
1st: 3
2nd: 6
3rd: 9
4th: 12
5th: 15

Total terms = 5

Answer: 5 terms (Finite)

Example 4: Does the sequence of even numbers (2, 4, 6, 8, ...) have a last term?

Even numbers go on indefinitely. You can always add 2 to get the next even number.

Because it never stops, it does not have a last term.

Answer: No, it is an Infinite Sequence.

Guided Practice

Try It Yourself!

Answer all 3 guided questions. Hints and solutions are available if you need them!

NOTE: Correct answers will turn GREEN so you know your answer is correct!

Mastery Check

Quick Quiz Time!

Answer all 10 questions in one go. Good luck!

Please answer ALL questions before submitting!

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Made for students who want to master Finite and Infinite Sequences