Maths Week Scotland 2026 - Challenge 7 - Sequence

Challenge 7 is all about a number sequence.

Maths teacher Chris Smith and pupils from Grange Academy are here to keep things in order.

The Maths Week Scotland Daily Challenges have been set by the Scottish Mathematical Council.

So here's the challenge:

This problem is all about a sequence.

The sequence starts 1, 1, 3, 4, 6, 9, 10, 16, 15, 25, 21, 36, 28, … and so on.

Can you work out the 200th term of the sequence?

• Think about how the numbers relate to each other.

• If you are unsure, focus on any patterns you recognise.

• You could try representing the numbers visually.

Worked out the answer? Here's how you can do it.

Step 1

This might be thought of as a trick question because it’s not one sequence but two sequences, disguised as one with alternating terms, like this:

1, 3, 6, 10, 15, 21, 28 , …

1, 4, 9, 16, 25, 36, …

Step 2

Representing the numbers visually makes it more obvious that there are two sequences.

• One is triangular numbers, (1, 3, 6, 10, 15…).
• The other is square numbers, (1, 4, 9, 16, 25…).

Step 3

So the 200th term of the original sequence will be the 100th term of the lower sequence.

This will be the 100th square number.

100² = 10,000

The 200th term of the whole sequence is 10,000.