Iteration

What you'll learn

1. 1

   Iteration means repeating a rule to get closer to an answer — like guessing a number and then using a rule to improve your guess each time.

2. 2

   What does iteration mean?

3. 3

   Let's solve x² - 10 = 0 using iteration. Start with guess x₀ = 3. Use the rule: xₙ₊₁ = (xₙ + 10/xₙ)/2

4. 4

   Now try it yourself! Starting with x₀ = 4, use the same rule to find the next guess x₁ for √10.

5. 5

   Using x₀ = 4 and the rule xₙ₊₁ = (xₙ + 10/xₙ)/2, what is x₁?

6. 6

   If xₙ and xₙ₊₁ are the same (to 4 decimal places), what does that mean?

7. 7

   Iteration is like a game of 'getting warmer' — each step uses the previous guess to make a better one, until you hit the answer!