| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Marks | 3 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Geometric Sequences and Series |
| Type | Convergence conditions |
| Difficulty | Moderate -0.8 This is a straightforward pattern recognition question from C2. Part (i) requires identifying a repeating sequence (trivial observation), part (ii) requires knowing that geometric series converge when |r|<1 (direct recall), and part (iii) asks for the nth term of sequence A which appears to be 2^(n-1) based on pattern spotting. All parts are routine applications of basic definitions with no problem-solving or proof required. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04f Sequence types: increasing, decreasing, periodic1.04i Geometric sequences: nth term and finite series sum |
| A: | 1, | 2, | 4, | 32, | \(\ldots\) | ||
| B: | 20, | - 10, | 5, | - 2.5, | 1.25, | - 0.625, | \(\ldots\) |
| C: | 20, | 5, | 1, | 20, | 5, | \(\ldots\) |
| Answer | Marks |
|---|---|
| (iv) \(n-1\) | 1 mark |
| Answer | Marks |
|---|---|
| 1 mark | 3 marks total |
Question 4:
(ii) 1 mark
(iii) 1 mark
(iv) $n-1$ | 1 mark
1 mark
1 mark | 3 marks total4 Sequences A, B and C are shown below. They each continue in the pattern established by the given terms.
\begin{center}
\begin{tabular}{ l l l l l l l l l }
A: & 1, & 2, & 4, & 32, & $\ldots$ & & \\
B: & 20, & - 10, & 5, & - 2.5, & 1.25, & - 0.625, & $\ldots$ \\
C: & 20, & 5, & 1, & 20, & 5, & $\ldots$ & \\
\end{tabular}
\end{center}
(i) Which of these sequences is periodic?\\
(ii) Which of these sequences is convergent?\\
(iii) Find, in terms of $n$, the $n$th term of sequence A .
\hfill \mbox{\textit{OCR MEI C2 Q4 [3]}}