| Exam Board | OCR MEI |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2007 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sigma notation: direct numerical evaluation |
| Difficulty | Easy -1.3 Part (i) requires simple substitution into a recurrence relation (t₂ = 2(3) + 5 = 11, t₃ = 2(11) + 5 = 27), which is purely mechanical. Part (ii) involves evaluating a small sum by direct calculation (1×2 + 2×3 + 3×4 = 20), requiring no formula knowledge. Both parts are routine drill exercises with minimal problem-solving, significantly easier than typical A-level questions. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(t_2 = 11\), \(t_3 = 27\) | B1 B1 | One mark each |
| (ii) \(1(2) + 2(3) + 3(4) = 2 + 6 + 12 = 20\) | M1 A1 | M1 for attempt to substitute \(k = 1, 2, 3\) |
## Question 4:
**(i)** $t_2 = 11$, $t_3 = 27$ | B1 B1 | One mark each
**(ii)** $1(2) + 2(3) + 3(4) = 2 + 6 + 12 = 20$ | M1 A1 | M1 for attempt to substitute $k = 1, 2, 3$
---4 (i) Find the second and third terms of the sequence defined by the following.
$$\begin{aligned}
t _ { n + 1 } & = 2 t _ { n } + 5 \\
t _ { 1 } & = 3
\end{aligned}$$
(ii) Find $\sum _ { k = 1 } ^ { 3 } k ( k + 1 )$.
\hfill \mbox{\textit{OCR MEI C2 2007 Q4 [4]}}