Find the jump between the numbers, then keep going. Watch tile patterns grow and work out what comes 10th without drawing them all.
Find the jump between the numbers, then make it once more.
Find the jump: the difference between two numbers side by side.
Same jump every time? Keep adding it on.
Picture 10 is picture 1 plus 9 jumps.
The rule starts with jump × n, then adds or takes away to fit.
Square numbers
1, 4, 9, 16, 25 …
Doubling
1, 2, 4, 8, 16 …
Triangle numbers
1, 3, 6, 10, 15 …
Work out the jump between each pair of numbers side by side. If it's the same every time, add it on again. If the jumps change, look at how they change: in square numbers they grow by 2 each time.
Start with the first term and add the jump 9 times, not 10: from the 1st to the 10th there are only 9 jumps. For 3, 5, 7, the 10th term is 3 + 9 × 2 = 21.
n is the position in the sequence. Put in n = 1, 2, 3 and you get 4, 7, 10. The number in front of n is the jump, so compare the sequence with that times table and see how far it is from it.
Children continue simple counting patterns at about 5 to 7, find the jump and missing numbers at about 7 to 9, and work out the 10th term and rules like 3n + 1 at about 10 to 12.