Moderate -0.8 This is a straightforward recurrence relation question requiring only direct calculation of four terms and their sum. No conceptual insight needed—just substitute values sequentially (u₁=2, u₂=10/4=2.5, u₃=10/6.25=1.6, u₄=10/2.56≈3.906) and add them up. Simpler than average A-level questions which typically require more problem-solving or multiple techniques.
1 A sequence is defined by \(u _ { 1 } = 2\) and \(u _ { k + 1 } = \frac { 10 } { u _ { k } ^ { 2 } }\).
Calculate \(\sum _ { k = 1 } ^ { 4 } u _ { k }\).
\(2 + u_2 + u_3 + u_4\) (must be the sum of 4 terms only)
M1dep*
\(10.00625\) or \(\frac{1601}{160}\) or \(101\frac{1}{80}\) cao isw
A1
Guidance:
NB \(2.5, 1.6, 3.90625\) or \(\frac{10}{4}, \frac{8}{5}, \frac{125}{32}\) may be implied by e.g. sight of \(3.9\) and answer of \(10.0\)
NB \(2.5, 1.1, 0.625\) scores M0M0
B3 if unsupported
# Question 1
$u_1 = 10$, $u_2 = \frac{10}{2.5^2}$, $u_3 = \frac{10}{1.6^2}$ | M1*
$2 + u_2 + u_3 + u_4$ (must be the sum of 4 terms only) | M1dep*
$10.00625$ or $\frac{1601}{160}$ or $101\frac{1}{80}$ cao isw | A1
**Guidance:**
NB $2.5, 1.6, 3.90625$ or $\frac{10}{4}, \frac{8}{5}, \frac{125}{32}$ may be implied by e.g. sight of $3.9$ and answer of $10.0$
NB $2.5, 1.1, 0.625$ scores M0M0
B3 if unsupported
1 A sequence is defined by $u _ { 1 } = 2$ and $u _ { k + 1 } = \frac { 10 } { u _ { k } ^ { 2 } }$.\\
Calculate $\sum _ { k = 1 } ^ { 4 } u _ { k }$.
\hfill \mbox{\textit{OCR MEI C2 Q1 [3]}}