| Exam Board | Edexcel |
|---|---|
| Module | C12 (Core Mathematics 1 & 2) |
| Year | 2016 |
| Session | January |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Recurrence relation: evaluate sum |
| Difficulty | Easy -1.2 This is a straightforward recurrence relation question requiring only direct substitution to find u₂ and u₃, then simple addition of four terms. It tests basic understanding of sequence notation and summation but involves no problem-solving, pattern recognition, or algebraic manipulation beyond arithmetic. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(u_2 = 2\times2-6=-2\) | M1 | Attempt to use given formula correctly at least once; implied by correct \(u_2\) or correct \(u_3\) following from their \(u_2\) |
| \(u_3 = 2\times(-2)-6=-10\) or \(u_3=2\times(2\times2-6)-6=-10\) | A1 | \(u_3\) correct and no incorrect work seen |
| Answer | Marks | Guidance |
|---|---|---|
| Working | Mark | Guidance |
| \(\sum_{i=1}^{4}u_i = 2+(-2)+(-10)\) | M1 | Uses sum of 3 numerical terms from part (a); attempting to sum an AP is M0 |
| \(+(-26)\) | A1ft | Obtains \(u_4\) correctly (may be attempted in part (a)) and adds to sum of first three terms |
| \(=-36\) | A1 | \(-36\) cao (\(-36\) implies both A marks) |
## Question 1:
### Part (a):
| Working | Mark | Guidance |
|---------|------|----------|
| $u_2 = 2\times2-6=-2$ | M1 | Attempt to use given formula correctly at least once; implied by correct $u_2$ or correct $u_3$ following from their $u_2$ |
| $u_3 = 2\times(-2)-6=-10$ or $u_3=2\times(2\times2-6)-6=-10$ | A1 | $u_3$ correct **and no incorrect work seen** |
### Part (b):
| Working | Mark | Guidance |
|---------|------|----------|
| $\sum_{i=1}^{4}u_i = 2+(-2)+(-10)$ | M1 | Uses sum of 3 numerical terms from part (a); attempting to sum an AP is M0 |
| $+(-26)$ | A1ft | Obtains $u_4$ correctly (may be attempted in part (a)) and adds to sum of first three terms |
| $=-36$ | A1 | $-36$ cao ($-36$ implies both A marks) |
**Special Cases:** Candidates attempting $u_2+u_3+u_4+u_5$ — allow M1 only. Mis-copying one term from (a) into (b) — allow M1 only.
---\begin{enumerate}
\item A sequence of numbers $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ satisfies
\end{enumerate}
$$u _ { n + 1 } = 2 u _ { n } - 6 , \quad n \geqslant 1$$
Given that $u _ { 1 } = 2$\\
(a) find the value of $u _ { 3 }$\\
(b) evaluate $\sum _ { i = 1 } ^ { 4 } u _ { i }$\\
\hfill \mbox{\textit{Edexcel C12 2016 Q1 [5]}}