Math · Stage 6

Find general nth-term rules and sum series

Every straight-climbing sequence hides a rule: the step is the number on n, the start fixes the rest. Know the rule and you can leap to the 100th term — or add a whole run of numbers in one tidy line.

✦ Math📘 Stage 6 · S6⏱ ~14 min🧒 Ages 10–12★ Free to start

I can find general nth-term rules and sum series.

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Kavi's One-Line Trick 🪄

Kavi's teacher said, “Add every number from 1 to 100!” 😮 While friends scribbled, Kavi grinned. “Pair them up: 1 + 100, 2 + 99, 3 + 98 … each pair makes 101, and there are 50 pairs — so the whole lot is 50 × 101 = 5050!” One line, done. “Every sequence hides a rule,” hooted Kavi, “and a tidy rule lets you jump to the nth term or add a long run of numbers all at once.”

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What your child will learn

1Every term has a position number nThis is the sequence 3, 7, 11, 15, 19, 23 (the lit-up numbers). Each one sits at a position: n = 1, 2, 3, … The jump from term to term — the step — is 4. That step is the secret to the rule.

2Read the step, then adjust the startThe step (how much it jumps each time) is the number in front of n. Then adjust: start − step tells you the + or − on the end. Tap a row to hear it.

3Add a whole run in ONE lineYou want 2 + 4 + 6 + … + 20. Tap each card — one way is a long slog, the other is a single step.

4Three sums worth memorisingSpot one of these shapes and the answer is a single line. Tap a row to hear it.

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A peek inside

Sequence 5, 8, 11, 14, … Find the nth-term rule, then the 10th term.

step is 3, first term is 5, so nth term = 3n + (5 − 3) = 3n + 2; then put n = 10: 3×10 + 2

Try this at home: Apply the rule: nth term = 4n − 1. Find the <b>6th</b> term → __

Ready to play and learn?

Start the free interactive lesson, or print the handout for screen-free play.

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Part of Math · Stage 6 · S6 on KAVI Academy — a secular, whole-child learning platform for ages 5–12.