A-LevelMathematicsNumerical methods9709/21 · May/June 2017 · Q46 Marks
The sequence of values given by the iterative formula xn+1 = (2x_n² + x_n + 9) / (x_n + 1)² with x₁ = 2, converges to α.
- (i)Find the value of α correct to 2 decimal places, giving the result of each iteration to 4 decimal places.[3]
- (ii)Determine the exact value of α.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.
- [M1] Use iteration correctly at least once
- [A1] Obtain final answer 2.08
- [A1] Show sufficient iterations to 4 dp to justify answer or show sign change in interval (2.075, 2.085)
- [B1] State or clearly imply equation x = (2x² + x + 9) / (x+1)² or same equation using α
- [M1] Carry out relevant simplification
- [A1] Obtain √9
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