AI generatedAlgebraGCSE Higher

Using an iteration formula

Calculate successive values from a starting value.

  • Use the previous answer as the next input. Keep unrounded calculator values.
  • Round only the values you report.
  • Convergence means successive values approach a limit; a few matching digits alone are not a proof.

Example 1

Starting with , find to 3 d..

Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.

Example 2

Starting with , find to 3 d..

Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.

Your turn

Question 1

Starting with , find to 3 d..

Check answer
Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.
Question 2

Starting with , find to 3 d..

Check answer
Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.
Question 3

Starting with , find to 3 d..

Check answer
Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.
Question 4

Starting with , find to 3 d..

Check answer
Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.
Question 5

Starting with , find to 3 d..

Check answer
Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.Substitute the previous unrounded value. Keep the calculator value for the next step.
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