| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Year | 2006 |
| Session | June |
| 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 only direct substitution to find terms and simple addition for the sum. Part (a) involves two basic calculations using the given formula, and part (b) requires finding two more terms and adding five numbers together. No problem-solving insight or complex manipulation is needed—purely mechanical application of a given rule. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Marks | Guidance |
| (a) \(a_2 = 4\) | B1 | |
| \(a_3 = 3 \times a_2 - 5 = 7\) | B1ft | Follow through their \(a_2\) but must be a value. \(3\times4-5\) is B0. Give wherever first seen |
| (b) \(a_4 = 3a_3 - 5 (= 16)\) and \(a_5 = 3a_4 - 5 (= 43)\) | M1 | For two further attempts to use \(a_{n+1} = 3a_n - 5\). Condone arithmetic slips |
| \(3 + 4 + 7 + 16 + 43\) | M1 | For attempting to add 5 relevant terms. Follow through their \(a_2 - a_5\). Use of arithmetic series formulae is M0A0 but could get 1st M1 if \(a_4\) and \(a_5\) correctly attempted |
| \(= 73\) | A1cao |
## Question 4:
| Answer/Working | Marks | Guidance |
|---|---|---|
| **(a)** $a_2 = 4$ | B1 | |
| $a_3 = 3 \times a_2 - 5 = 7$ | B1ft | Follow through their $a_2$ but must be a value. $3\times4-5$ is B0. Give wherever first seen |
| **(b)** $a_4 = 3a_3 - 5 (= 16)$ and $a_5 = 3a_4 - 5 (= 43)$ | M1 | For two further attempts to use $a_{n+1} = 3a_n - 5$. Condone arithmetic slips |
| $3 + 4 + 7 + 16 + 43$ | M1 | For attempting to add 5 relevant terms. Follow through their $a_2 - a_5$. Use of arithmetic series formulae is M0A0 but could get 1st M1 if $a_4$ and $a_5$ correctly attempted |
| $= 73$ | A1cao | |
---4. A sequence $a _ { 1 } , a _ { 2 } , a _ { 3 } , \ldots$ is defined by
$$\begin{aligned}
& a _ { 1 } = 3 \\
& a _ { n + 1 } = 3 a _ { n } - 5 , \quad n \geqslant 1 .
\end{aligned}$$
\begin{enumerate}[label=(\alph*)]
\item Find the value of $a _ { 2 }$ and the value of $a _ { 3 }$.
\item Calculate the value of $\sum _ { r = 1 } ^ { 5 } a _ { r }$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 2006 Q4 [5]}}