Step 1: Recognise the numbers.
Each number is a perfect square. 121 is $11^2$, 144 is $12^2$, 289 is $17^2$, 324 is $18^2$, 529 is $23^2$, 576 is $24^2$.
Step 2: List the base numbers.
The bases are 11, 12, 17, 18, 23, 24.
Step 3: Find the steps.
From 11 to 12 is plus 1. From 12 to 17 is plus 5. From 17 to 18 is plus 1. From 18 to 23 is plus 5. From 23 to 24 is plus 1.
Step 4: Next step.
The pattern is plus 1, plus 5, repeating. After plus 1 the next is plus 5, so $24 + 5 = 29$.
Step 5: Square it.
So the next number is \[ 29^2 = 841 \]
Step 6: Conclusion.
The missing number is 841.
Answer: 841