Moderate -0.8 This is a straightforward recurrence relation requiring simple substitution to calculate three terms, followed by a basic observation about convergence behavior. The arithmetic is elementary (squaring and division), and identifying the limiting behavior requires only direct computation and pattern recognition rather than formal analysis.
2 A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = 10 \\
u _ { r + 1 } & = \frac { 5 } { u _ { r } ^ { 2 } }
\end{aligned}$$
Calculate the values of \(u _ { 2 } , u _ { 3 }\) and \(u _ { 4 }\).
What happens to the terms of the sequence as \(r\) tends to infinity?
\(0.05, 2000, 1.25 \times 10^{-6}\) or \(\frac{1}{20}, 2000, \frac{1}{800000}\) o.e.
B2
B1 for two correct
divergent
B1
allow "alternate terms tend to zero and to infinity" o.e.
$0.05, 2000, 1.25 \times 10^{-6}$ or $\frac{1}{20}, 2000, \frac{1}{800000}$ o.e. | B2 | B1 for two correct
divergent | B1 | allow "alternate terms tend to zero and to infinity" o.e. | do not allow "oscillating", "getting bigger and smaller", "getting further apart"
2 A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = 10 \\
u _ { r + 1 } & = \frac { 5 } { u _ { r } ^ { 2 } }
\end{aligned}$$
Calculate the values of $u _ { 2 } , u _ { 3 }$ and $u _ { 4 }$.\\
What happens to the terms of the sequence as $r$ tends to infinity?
\hfill \mbox{\textit{OCR MEI C2 2011 Q2 [3]}}