What comes next?
You will choose a rule for a number sequence and use it to suggest the next entry. Several rules can fit a short list, so explaining the rule is part of the thinking.
- Maths
- Starter
- About 10 minutes
Help needed: yes for setup, checking and any preparation of paper or small items
What you need
- Paper
- A pencil
The rule
No calculators.
How to do it
- Write the sequence 2, 4, 8, 16 with a gap after it.
- Compare each neighbouring pair.
- Choose a rule that fits all three changes.
- Use that rule to fill the gap.
- Check the whole sequence aloud without a calculator.
Why it works
Doubling each entry gives 2, 4, 8, 16, 32. The rule is multiplication by two, and it works at every shown step. However, a finite list does not force only one possible rule. You could invent a more complicated rule that gives a different next entry. In this challenge, a useful answer states a clear rule and checks it against all the evidence, rather than claiming a guess must be uniquely right.
Make it harder
- Start from 3 with the same rule.
- Find an adding rule for another sequence.
- Invent a different rule that fits the four shown entries.
Ask Taz
- Why does doubling fit every step here?
- Why can a short sequence have different continuations?
- Why must I test a rule on all the entries?
Before you start
Let the learner describe the change before you name multiplication. Accept an alternative when they can state and check its rule. This practises reasoning from examples without turning a short list into proof. Ask at dinner: “Would one more number make your chosen rule more convincing, and why?”
Taz is an AI and can be wrong, so check what matters. Read how safety works on Taz.
Show us yours
Film your hands and what you made, not your face or name. If you are under 18, ask a parent or guardian before posting anywhere else.
Common questions
How much preparation does this need?
Use the household items above and begin with one small example. A helper can prepare the space or checking sheet while you choose the prediction. The time is an estimate and includes a little room to repeat.
What if we get different answers?
Compare the rule, the method and what each person recorded. A difference can reveal a changed assumption or an ordinary variation, so check before deciding someone must be wrong.
Do I have to share online?
No. Discuss the work at home first. Public sharing is optional and follows the privacy wording above.
More to try
See all Taz Challenges, or look through the science labs. One place for every why. Start exploring at aitaz.com