| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2010 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Moderate -0.8 This is a straightforward arithmetic sequence question requiring basic substitution (part i), application of the standard sum formula (part ii), and simple equation solving (part iii). All techniques are routine C2 content with no problem-solving insight needed, making it easier than average but not trivial since it requires correct formula application. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| \(u_1 = 6, u_2 = 11, u_3 = 16\) | B1 | State 6, 11, 16 |
| Answer | Marks | Guidance |
|---|---|---|
| \(S_{40} = \frac{40}{2}(2 \times 6 + 39 \times 5)\) | M1 | Show intention to sum the first 40 terms of a sequence |
| M1 | Attempt sum of their AP from (i), with \(n = 40\), \(a\) = their \(u_1\) and \(d\) = their \(u_2 - u_1\) | |
| \(= 4140\) | A1 | Obtain 4140 |
| Answer | Marks | Guidance |
|---|---|---|
| \(w_3 = 56\) | B1 | State or imply \(w_3 = 56\) |
| \(5p + 1 = 56\) or \(6 + (p-1) \times 5 = 56\) | M1 | Attempt to solve \(u_p = k\) |
| \(p = 11\) | A1 | Obtain \(p = 11\) |
## Question 4:
### Part (i)
| $u_1 = 6, u_2 = 11, u_3 = 16$ | B1 | State 6, 11, 16 |
### Part (ii)
| $S_{40} = \frac{40}{2}(2 \times 6 + 39 \times 5)$ | M1 | Show intention to sum the first 40 terms of a sequence |
| | M1 | Attempt sum of their AP from (i), with $n = 40$, $a$ = their $u_1$ and $d$ = their $u_2 - u_1$ |
| $= 4140$ | A1 | Obtain 4140 |
### Part (iii)
| $w_3 = 56$ | B1 | State or imply $w_3 = 56$ |
| $5p + 1 = 56$ or $6 + (p-1) \times 5 = 56$ | M1 | Attempt to solve $u_p = k$ |
| $p = 11$ | A1 | Obtain $p = 11$ |
---4 A sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by $u _ { n } = 5 n + 1$.\\
(i) State the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$.\\
(ii) Evaluate $\sum _ { n = 1 } ^ { 40 } u _ { n }$.
Another sequence $w _ { 1 } , w _ { 2 } , w _ { 3 } , \ldots$ is defined by $w _ { 1 } = 2$ and $w _ { n + 1 } = 5 w _ { n } + 1$.\\
(iii) Find the value of $p$ such that $u _ { p } = w _ { 3 }$.
\hfill \mbox{\textit{OCR C2 2010 Q4 [7]}}