| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Real-world AP: find n satisfying a condition |
| Difficulty | Moderate -0.8 This is a straightforward application of arithmetic and geometric series formulas to real-world contexts. Part (i) requires summing an arithmetic sequence and solving a quadratic equation, while part (ii) involves geometric series with standard doubling patterns. All techniques are routine C2 content with clear scaffolding and no novel problem-solving required. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum |
# Question 1
**Part (i)**
M1: Correct use of AP formula with $a = 10$ and $d = 10$
A1: $n(5 + 5n)$ or $5n(n + 1)$ or $5(n^2 + n)$ or $(5n^2 + 5n)$
M1: $10n^2 + 10n - 20700 = 0$
A1: $45$ c.a.o.
**Part (ii)**
M1: Correct use of GP formula with $a = 5$, $r = 2$
A1: $5(2^n - 1)$ o.e. $= 2621435$
M1: $2^n = 524288$ www
DM1: (dependent on previous M1)
A1: $19$ c.a.o.
**Alternative/Additional Guidance:**
Or $\left(\frac{2 \times 10 + 5 \times 10}{2}\right)$ or $\left(\frac{10 + 60}{2}\right)$
M1 for $5(1 + 2 + \ldots 28)$ or $5(2^9 - 1)$ o.e.
"$S$" need not be simplified1
\begin{enumerate}[label=(\roman*)]
\item In a 'Make Ten' quiz game, contestants get $\pounds 10$ for answering the first question correctly, then a further $\pounds 20$ for the second question, then a further $\pounds 30$ for the third, and so on, until they get a question wrong and are out of the game.\\
(A) Haroon answers six questions correctly. Show that he receives a total of $\pounds 210$.\\
(B) State, in a simple form, a formula for the total amount received by a contestant who answers $n$ questions correctly.
Hence find the value of $n$ for a contestant who receives $\pounds 10350$ from this game.
\item In a 'Double Your Money' quiz game, contestants get $\pounds 5$ for answering the first question correctly, then a further $\pounds 10$ for the second question, then a further $\pounds 20$ for the third, and so on doubling the amount for each question until they get a question wrong and are out of the game.\\
(A) Gary received $\pounds 75$ from the game. How many questions did he get right?\\
(B) Bethan answered 9 questions correctly. How much did she receive from the game?\\
(C) State a formula for the total amount received by a contestant who answers $n$ questions correctly.
Hence find the value of $n$ for a contestant in this game who receives $\pounds 2621435$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI C2 Q1 [12]}}