| Exam Board | Edexcel |
|---|---|
| Module | C1 (Core Mathematics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find n satisfying a condition |
| Difficulty | Moderate -0.3 This is a standard C1 arithmetic sequence question requiring pattern recognition (finding nth term), sum of arithmetic series, and solving a quadratic inequality. While multi-part with 12 marks total, each step follows routine procedures: spotting the sequence 4,7,10 gives first term and common difference, applying standard sum formula, then algebraic manipulation. The inequality in part (c) is given to prove rather than derive independently, reducing difficulty. Slightly easier than average due to scaffolding and standard techniques. |
| Spec | 1.02g Inequalities: linear and quadratic in single variable1.04e Sequences: nth term and recurrence relations1.04h Arithmetic sequences: nth term and sum formulae |
Ann has some sticks that are all of the same length. She arranges them in squares and has made the following 3 rows of patterns:
Row 1 $\square$
Row 2 $\square\square$
Row 3 $\square\square\square$
She notices that 4 sticks are required to make the single square in the first row, 7 sticks to make 2 squares in the second row and in the third row she needs 10 sticks to make 3 squares.
\begin{enumerate}[label=(\alph*)]
\item Find an expression, in terms of $n$, for the number of sticks required to make a similar arrangement of $n$ squares in the $n$th row. [3]
\end{enumerate}
Ann continues to make squares following the same pattern. She makes 4 squares in the 4th row and so on until she has completed 10 rows.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{1}
\item Find the total number of sticks Ann uses in making these 10 rows. [3]
\end{enumerate}
Ann started with 1750 sticks. Given that Ann continues the pattern to complete $k$ rows but does not have sufficient sticks to complete the $(k + 1)$th row,
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item show that $k$ satisfies $(3k - 100)(k + 35) < 0$. [4]
\item Find the value of $k$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel C1 Q9 [12]}}