This introduction covers Zeroing In within Iteration for GCSE Mathematics. Revise Iteration in Algebra for GCSE Mathematics with 9 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 4 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
Zeroing In
Some equations can't be solved exactly. But we can get closer and closer to the answer by "iterating" - using each answer to calculate a better one. It's like zooming in on a target, getting more accurate each time.
Practice questions for Iteration
What is the purpose of using an iterative formula in mathematics?
A student uses the iterative formula xₙ₊₁ = xₙ² − 2 with x₀ = 0.5 and obtains the sequence 0.5, −1.75, 1.0625, −0.871, −1.241, ... Explain what is happening.
Quick recall flashcards
Sum Formula
S_n = a(r^n - 1)/(r - 1) where r is common ratio
Iteration Process
Put xₙ into formula to get xₙ₊₁. Repeat until values converge (settle down).