L2 · Finite and infinite sequences

Learning goal

“I can tell whether a sequence is finite - it has a definite end and a last term - or infinite - it goes on forever - and I know the three dots (…) show that a sequence keeps going.”

Finite sequence — a sequence that has a definite end. It has a last term you can point to, like a countdown: 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0.

Infinite sequence — a sequence that never ends. There is no last term, like the natural numbers: 1, 2, 3, 4, …

Ellipsis (…) — the three dots written at the end of a sequence to show it keeps going and has no last term.

Worked example

Look at the sequence 20, 18, 16, 14, 12, 10. Step 1: Read to the end of the list. The list stops at 10. Step 2: 10 is the LAST term - there is no term after it in this sequence. Step 3: A sequence with a definite end and a last term is a finite sequence. Say it plainly: finite means it ENDS. If you can point at the last term, the sequence is finite - a countdown is the classic example.

Check yourself — explain it

Why is 5, 10, 15, 20, 25 a finite sequence?

Paired problem — example still visible

Is 100, 90, 80, 70 finite or infinite? -> Finite - as written it ends at 70, its last term

Faded completion — last step is yours

"A sequence with a definite end and a last term is called a ___ sequence." -> finite

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10 scored questions with a 3-rung hint ladder. Mastery needs 8/10 plus both gate questions.

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