Iteration

The Maths Habit

Pick any number. Halve it, then add 10. Do the same to your answer, again and again. What do you notice?

Everyone gets closer and closer to 20

Iteration
Repeating a process, with each answer becoming the next input.

xnthe value you have xn+1the next value

xn+1 = xn + 94

x0 = 1

1

x0 = 2. Find x1, x2 and x3.

xn+1 = xn + 103

244.6674.889

(2 + 10) ÷ 3 = 4

(4 + 10) ÷ 3 = 4.667

x0 = 6. Find x1, x2 and x3.

xn+1 = xn + 63

643.3333.111

x0 = 2. Find x1, x2 and x3.

xn+1 = xn + 103

244.6674.889

x0 = 3. Find x1, x2 and x3.

xn+1 = √xn + 12

33.8733.9843.998

Iteration worksheet, page 1

Iteration worksheet, page 2

Answer sheet

  1. The values from xn+1 = xn + 124 get closer and closer to one number. What is it, and why?

    4, because (4 + 12) ÷ 4 = 4

  2. Show that x3 − 5x − 3 = 0 can be rearranged to x = 3√5x + 3

    x3 = 5x + 3

  1. x0 = 1 and xn+1 = xn + 113
    Find x1 and x2

    x1 = 4, x2 = 5

  2. x0 = 2 and xn+1 = √xn + 10
    Find x1 and x2 to 3 decimal places.

    x1 = 3.464, x2 = 3.669

  3. x0 = 6 and xn+1 = xn + 184
    Find x1. What do you notice?

    x1 = 6, it stays at 6
Exit tickets to print