| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2018 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: evaluate sum |
| Difficulty | Moderate -0.8 This is a straightforward recurrence relation question requiring simple substitution to find u₂ and u₃, followed by basic arithmetic to evaluate a small summation. Part (a) involves direct application of the formula twice, and part (b) requires computing four terms and summing simple expressions. No problem-solving insight needed—purely mechanical calculation with standard Core 1/2 content. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(u_2 = -1\), \(u_3 = 5\) | B1, B1 | Can score as part of calculation in (b) if \(-1\) and \(5\) are clearly second and third terms |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(u_4 = 2 - 3 \times\text{"5"} (= -13)\) | M1 | Correct attempt at 4th term, may be implied by calculation below |
| \(\sum_{r=1}^{4}(r - u_r) = \pm\{(1-1)+(2-\text{"-1"})+(3-\text{"5"})+(4-\text{"-13"})\}\) or \(\sum_{r=1}^{4}r - \sum_{r=1}^{4}u_r = \pm\{(1+2+3+4)-(1+\text{"-1"}+\text{"5"}+\text{"-13"})\}\) | dM1 | Correct method for sum. Allow minor slips. Dependent on first method mark |
| \(= 18\) | A1 | cso |
## Question 2:
### Part (a):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $u_2 = -1$, $u_3 = 5$ | B1, B1 | Can score as part of calculation in (b) if $-1$ and $5$ are clearly second and third terms |
### Part (b):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $u_4 = 2 - 3 \times\text{"5"} (= -13)$ | M1 | Correct attempt at 4th term, may be implied by calculation below |
| $\sum_{r=1}^{4}(r - u_r) = \pm\{(1-1)+(2-\text{"-1"})+(3-\text{"5"})+(4-\text{"-13"})\}$ or $\sum_{r=1}^{4}r - \sum_{r=1}^{4}u_r = \pm\{(1+2+3+4)-(1+\text{"-1"}+\text{"5"}+\text{"-13"})\}$ | dM1 | Correct method for sum. Allow minor slips. Dependent on first method mark |
| $= 18$ | A1 | cso |
---2. A sequence is defined by
$$\begin{aligned}
u _ { 1 } & = 1 \\
u _ { n + 1 } & = 2 - 3 u _ { n } \quad n \geqslant 1
\end{aligned}$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $u _ { 2 }$ and the value of $u _ { 3 }$
\item Calculate the value of $\sum _ { r = 1 } ^ { 4 } \left( r - u _ { r } \right)$\\
□
\end{enumerate}
\hfill \mbox{\textit{Edexcel C12 2018 Q2 [5]}}