Topic/Skill Definition/Tips Example
Topic: Iteration
1. Iteration The act of repeating a process over and x 1=4
over again, often with the aim of x 2=√ 3 ×4 +6=4.242640 …
approximating a desired result more x 3=√ 3 ×4.242640 …+ 6=4.357576 …
closely.
Recursive Notation: x n+1= √3 x n +6
2. Iterative To create an iterative formula, rearrange Use an iterative formula to find the
Method an equation with more than one x term to positive root of x 2−3 x−6=0 to 3
make one of the x terms the subject. decimal places.
x 1=4
You will be given the first value to
substitute in, often called x 1. Answer:
x 2=3 x+ 6
Keep substituting in your previous x=√ 3 x+ 6
answer until your answers are the same to So x n+1= √3 x n +6
a certain degree of accuracy. This is called
converging to a limit. x 1=4
Use the ‘ANS’ button on your calculator to x 2=√ 3 ×4 +6=4.242640 …
keep substituting in the previous answer. x 3=√ 3 ×4.242640 …+ 6=4.357576 …
Keep repeating…
x 7=4.372068..=4.372 ( 3 dp )
x 8=4.372208 …=4.372(3 dp)
Subject: Maths So answer is x=4.372(3 dp)
Mr A. Coleman Glyn School
Topic: Iteration
1. Iteration The act of repeating a process over and x 1=4
over again, often with the aim of x 2=√ 3 ×4 +6=4.242640 …
approximating a desired result more x 3=√ 3 ×4.242640 …+ 6=4.357576 …
closely.
Recursive Notation: x n+1= √3 x n +6
2. Iterative To create an iterative formula, rearrange Use an iterative formula to find the
Method an equation with more than one x term to positive root of x 2−3 x−6=0 to 3
make one of the x terms the subject. decimal places.
x 1=4
You will be given the first value to
substitute in, often called x 1. Answer:
x 2=3 x+ 6
Keep substituting in your previous x=√ 3 x+ 6
answer until your answers are the same to So x n+1= √3 x n +6
a certain degree of accuracy. This is called
converging to a limit. x 1=4
Use the ‘ANS’ button on your calculator to x 2=√ 3 ×4 +6=4.242640 …
keep substituting in the previous answer. x 3=√ 3 ×4.242640 …+ 6=4.357576 …
Keep repeating…
x 7=4.372068..=4.372 ( 3 dp )
x 8=4.372208 …=4.372(3 dp)
Subject: Maths So answer is x=4.372(3 dp)
Mr A. Coleman Glyn School
