A-LevelMathematicsNumerical methods9709/23 · Oct/Nov 2020 · Q55 Marks
The sequence of values given by the iterative formula xₙ₊₁ = (6+8xₙ)/(8+xₙ²) with initial value x₁ = 2 converges to α.
- (a)Use the iterative formula to find the value of α correct to 4 significant figures. Give the result of each iteration to 6 significant figures.[3]
- (b)State an equation satisfied by α and hence determine the exact value of α.[2]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2020). The mark or mark type is shown in brackets.
- [M1] Use iteration correctly at least once Need to see 3 values including the starting values
- [A1] Obtain final answer 1.817 Answer required to exactly 4 significant figures
- [A1] Show sufficient iterations to 6 significant figures to justify answer or show sign change in interval [1.8165, 1.8175]
- [B1] State equation x = (6+8x)/(8+x²) or equivalent using α
- [B1] Obtain √6 or exact equivalent
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