| Exam Board | Pre-U |
|---|---|
| Module | Pre-U 9794/2 (Pre-U Mathematics Paper 2) |
| Year | 2012 |
| Session | June |
| Marks | 8 |
| Topic | Arithmetic Sequences and Series |
| Type | Sum of specific range of terms |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring standard formulas. Part (i) uses basic arithmetic progression properties to find the nth term, part (ii) applies the sum formula, and part (iii) is a simple application recognizing that 8n-3 matches the sequence form. All techniques are routine recall with minimal problem-solving, making it easier than average but not trivial due to the multi-step nature. |
| Spec | 1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (i)(a) \(u_1 = 5\), \(u_5 = 37\) implies \(4d = 32\) | M1, A1, M1 | |
| \(d = 8\); \(u_n = 8n - 3\) AEF | \A1 [4] | seen in either part |
| (i)(b) \(S_n = \frac{n}{2}(2 + 8n)\) AEF | M1, \A1 [2] | fit their \(d\) |
| (ii) \(S_{25} - S_4 = 2525 - 68 = 2457\) | M1, A1 [2] | [8] |
**(i)(a)** $u_1 = 5$, $u_5 = 37$ implies $4d = 32$ | M1, A1, M1 |
$d = 8$; $u_n = 8n - 3$ AEF | \A1 [4] | seen in either part
**(i)(b)** $S_n = \frac{n}{2}(2 + 8n)$ AEF | M1, \A1 [2] | fit their $d$
**(ii)** $S_{25} - S_4 = 2525 - 68 = 2457$ | M1, A1 [2] | [8] | Or equivalent\begin{enumerate}[label=(\roman*)]
\item An arithmetic sequence has first term 5 and fifth term 37.
\begin{enumerate}[label=(\alph*)]
\item Find an expression for $u_n$, the $n$th term of the sequence, in terms of $n$. [4]
\item Find an expression for $S_n$, the sum of the first $n$ terms of this sequence, in terms of $n$. [2]
\end{enumerate}
\item Hence, or otherwise, calculate $\sum_{n=5}^{25} (8n - 3)$. [2]
\end{enumerate}
\hfill \mbox{\textit{Pre-U Pre-U 9794/2 2012 Q6 [8]}}