| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find n satisfying a condition |
| Difficulty | Easy -1.2 This is a straightforward arithmetic sequence question requiring only direct application of standard formulas (nth term and sum). Part (a) uses a=20, d=2 to find u₅=28. Part (b) verifies S₈=1512 using the sum formula. Part (c) solves 20+2(n-1)>300 for n=141. All parts are routine calculations with no problem-solving insight required, making it easier than average. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(a = 20 \times 7 = 140, d = 2 \times 7 = 14\) | B1 | |
| \(u_5 = 140 + (4 \times 14) = 196\) | M1 A1 | |
| (b) \(S_8 = \frac{8}{2}[280 + (7 \times 14)] = 4 \times 378 = 1512\) | M1 A1 | |
| (c) \(140 + 14(n - 1) > 300\) | M1 | |
| \(n > \frac{160}{14} + 1\) | M1 | |
| \(n > 12\frac{3}{7} \therefore n = 13\) | A1 | (8) |
(a) $a = 20 \times 7 = 140, d = 2 \times 7 = 14$ | B1 |
$u_5 = 140 + (4 \times 14) = 196$ | M1 A1 |
(b) $S_8 = \frac{8}{2}[280 + (7 \times 14)] = 4 \times 378 = 1512$ | M1 A1 |
(c) $140 + 14(n - 1) > 300$ | M1 |
$n > \frac{160}{14} + 1$ | M1 |
$n > 12\frac{3}{7} \therefore n = 13$ | A1 | (8)7. As part of a new training programme, Habib decides to do sit-ups every day.
He plans to do 20 per day in the first week, 22 per day in the second week, 24 per day in the third week and so on, increasing the daily number of sit-ups by two at the start of each week.
\begin{enumerate}[label=(\alph*)]
\item Find the number of sit-ups that Habib will do in the fifth week.
\item Show that he will do a total of 1512 sit-ups during the first eight weeks.
In the $n$th week of training, the number of sit-ups that Habib does is greater than 300 for the first time.
\item Find the value of $n$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q7 [8]}}