Math · Stage 6
Find the rule of a sequence and its nth term
Spot the equal step that builds a sequence, write its nth-term rule like 4n − 1, and use that rule to jump straight to the 10th, 20th or 100th term without listing them all.
✦ Math📘 Stage 6 · S6⏱ ~14 min🧒 Ages 10–12★ Free to start
I can find the rule of a sequence and its nth term.
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Kavi and the Growing Staircase 🪜
Kavi hops up a magic staircase where every step is the same height taller than the last: 3, 7, 11, 15… "Once I know the step," Kavi hoots, "I don't have to climb every stair to know the 100th one — I can write a rule that jumps straight there! ⚡ The rule even tells me the step and where the staircase started."
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What your child will learn
1A sequence grows by an equal stepA sequence is a list of numbers that follow a rule. In 3, 7, 11, 15, 19, 23 every jump is the same size: +4. That equal jump is the term-to-term rule, also called the common difference. Find it by subtracting any term from the one after it: 7 − 3 = 4.
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3Each position has one termLine the sequence 5, 8, 11, 14, 17 up by position. Every bar is 3 taller than the one before — that steady climb is the common difference, and the nth-term rule 3n + 2 gives the height at any position n.
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A peek inside
Find the next term: 4, 9, 14, 19, …
check the step is equal: 9 − 4 = 5, 14 − 9 = 5 — common difference 5; so after 19 comes 19 + 5
Try this at home: Find the next term: 7, 11, 15, 19, __
Ready to play and learn?
Start the free interactive lesson, or print the handout for screen-free play.
Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.