Nth term – finding algebraic rules for number sequences

Mathematical Language Covered

  • Function
  • Simplest Form
  • Mathematically equivalent
  • Sequence

You will need:

  • One Scientific Calculator each  (I use Casio fx-83GT Plus)
  • A4 Card – the best type has one coloured side, the other white – cut into tenths. You will need 3 or 4 pieces per pupil.
  • A group which is already reasonably good at supporting one another
  • Class Whiteboard


  1. Walk the class slowly and carefully through the key presses needed to put the calculators in TABLE more. (Mode 3) – like all ICT inputs, some will inevitably get lost and panic – this is where it’s important for them to be used to getting support from each other.
  2. Once they can all see F(X)=, ask them to input 10 =
  3. For “Start”, stick to 1 all lesson.
  4. For “End”,  input 10 =
  5. For “Step” input 1 =
  6. Ask them to describe what they can see. Including the column headings. Remind them to “mouse” down to see the bottom section of the table. Write the F(X)=10 and the sequence on the board.
  7. Press AC to clear the table and start again. This time try F(X)=12. Ask how they could make it more interesting, let them experiment. My lot came up with larger numbers but still the whole sequence was all the same number.
  8. How can you make the numbers change? Someone might already know – discuss and try F(X)=2X. This is achieved by keying in 2ALPHA (= because the ( button has X above it.
  9. Describe and write on the board the sequence this creates.
  10. Try 6X-1, describe, discuss.

Creating the Puzzles

Give out 2 pieces of card each. Create your choice of sequence, write it on the coloured side of the card. On the back write F(X)= and the function you used.

Discuss boundries – numbers under 10. (I should have set more – no decimals and no division yet. But it did make life interesting!

As they produce the cards, check the function – if it isn’t in simplest form, then simplify it with them and write that version underneath. Point out that their friends won’t be able to guess any more complicated version of the rule. eg if the rule they used was F(X)= 2X+3X+1 then the friends will guess 5X+1

If you think any of them are quite difficult, give them one or two stars. This will let the pupils self-differentiate.

Solving the puzzles

Put the cards down SEQUENCE SIDE UP and the pupils choose which one they want to do. Try to guess the F(X), key your guess onto the calculator, can you make that exact sequence? Once you have made it, turn over and check the rule on the card. Then initial the front of the card to note that you have done it.


What was easy? What was more challenging? Do we need another lesson on this (My group decided they found the minus ones harder so we pencilled in a lesson on handling negative numbers.

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