Unit 1 · Topic 06 · Number System & Notation

Number Patterns and Sequences for Class 5

Hook

Ms. Rao wrote 3, 7, 11, 15, ___ on the board and asked for the next number.

Kabir guessed 16. Anaya guessed 19.

Only one of them had actually found the RULE — the other had just guessed a number that looked plausible.

The Story

"3, 7, 11, 15 — what comes next?" asked Ms. Rao.

Kabir said 16, because it came right after 15. Anaya disagreed. "Look at the GAPS between the numbers, not just the last one."

She worked it out: 7 − 3 = 4. 11 − 7 = 4. 15 − 11 = 4. "Every gap is exactly 4. So the next number should be 15 + 4 = 19."

"That's the right way to think about it," said Ms. Rao. "A number pattern isn't guessed from what LOOKS right — it's found by discovering the RULE that connects every term to the next one. Here, the rule is 'add 4 each time.'"

She gave them a trickier one: 2, 4, 8, 16, ___. Kabir tried subtraction first — 4−2=2, 8−4=4, 16−8=8. "The gaps aren't the same. Adding doesn't work here."

Anaya tried division instead: 4÷2=2, 8÷4=2, 16÷8=2. "Each number is DOUBLE the one before it! So the next is 16 × 2 = 32."

"Exactly — not every pattern is 'add the same amount.' Some patterns multiply by the same amount each time instead," said Ms. Rao.

She then wrote: 1, 4, 9, 16, 25, ___. "This one is neither simple addition nor simple multiplication. Look closer."

Kabir noticed: 1 is 1×1, 4 is 2×2, 9 is 3×3, 16 is 4×4, 25 is 5×5. "They're square numbers! The next one is 6×6 = 36."

"Wonderful," said Ms. Rao. "The real skill in finding a pattern is testing more than one idea — try the gaps first, then try ratios, then look for a shape like squares — until one of them actually fits EVERY term, not just the first two."

3, 7, 11, 15 — every gap is +4.

So What Just Happened?

A number pattern (sequence) follows a consistent RULE connecting each term to the next — the rule must be verified against every term, not just guessed from the last one.

An arithmetic pattern adds (or subtracts) the same fixed amount each time — check by finding the gap between consecutive terms.

A geometric pattern multiplies (or divides) by the same fixed amount each time — check by dividing consecutive terms.

Some patterns follow a special shape, like square numbers (1, 4, 9, 16, 25...) — recognising the shape of the numbers can reveal the rule when simple addition or multiplication doesn't fit.

Adding a fixed amount, or multiplying by a fixed amount.

Remember This

A number pattern follows a consistent rule linking every term to the next.
Arithmetic pattern: adds or subtracts the same fixed amount each time.
Geometric pattern: multiplies or divides by the same fixed amount each time.
Some patterns follow a shape, like square numbers.
Always check a candidate rule against EVERY term, not just the first two.

1, 4, 9, 16, 25 — each is a whole number times itself.

Try It Yourself

Create your own arithmetic pattern (pick a starting number and a fixed amount to add) and write the first 6 terms.

Look at the sequence 1, 3, 6, 10, 15 (triangular numbers) and try to figure out the rule connecting each term.

Word Bank

Sequence: An ordered list of numbers following a rule.
Term: One single number in a sequence.
Arithmetic pattern: A sequence formed by adding or subtracting the same amount each time.
Geometric pattern: A sequence formed by multiplying or dividing by the same amount each time.
Square number: A number formed by multiplying a whole number by itself.

Questions

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