Iteration
Teach Genie
Review Iteration by teaching Genie
Teach it back in your own words, spot gaps, and remember it better.
Iteration means repeatedly applying the same rule. In xn+1=2+6xn2x_{n+1}=2+\frac{6}{x_n^2}xn+1=2+xn26, xnx_nxn is the current value and xn+1x_{n+1}xn+1 is the next value.
A subscript is not a power, so x3x_3x3 means the term with subscript 333, not x3x^3x3. The first given value is called the starting value, usually x0x_0x0 or P0P_0P0.
Each use of the rule moves one step along the sequence: x0→x1→x2→x3x_0 \to x_1 \to x_2 \to x_3x0→x1→x2→x3. Always substitute the latest value back into the formula.
Question 1
3 marksThe number of rabbits in a field t t\,t days from now is Pt P_t\,Pt where
P0=220 P_0 = 220 P0=220 Pt+1=1.15(Pt−20) P_{t+1} = 1.15(P_t - 20) Pt+1=1.15(Pt−20)Iteration Revision Guide
Revision notes for AQA GCSE Maths Iteration: explanations and worked examples.