| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2014 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Easy -1.2 This is a straightforward arithmetic sequence question requiring only direct substitution into a given formula and application of the standard arithmetic series sum formula. Both parts are routine calculations with no problem-solving or conceptual challenge beyond basic recall. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(2, 5, 8\) | B1 | Obtain at least one correct value. Either stated explicitly or as part of a longer list, but must be in correct position e.g. \(-1, 2, 5\) is B0 |
| B1 | Obtain all three correct values. Ignore any subsequent values if given |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(S_{40} = \frac{40}{2}(2 \times 2 + 39 \times 3)\) | B1* | Identify AP with \(a = 2\), \(d = 3\). Could be stated, listing further terms linked by \(+\) sign or by recognisable attempt at any formula for AP including attempt at \(u_{40}\) |
| \(= 2420\) | M1d* | Attempt to sum first 40 terms of the AP. Must use correct formula with \(a = 2\) and \(d = 3\). If using \(\frac{1}{2}n(a+l)\) then must be valid attempt at \(l\). Could use \(3\sum n - \sum 1\), but M0 for \(3\sum n - 1\) |
| A1 | Obtain 2420. Either from formula or from manual summing of 40 terms |
# Question 2:
## Part (i)
| Answer | Mark | Guidance |
|--------|------|----------|
| $2, 5, 8$ | B1 | Obtain at least one correct value. Either stated explicitly or as part of a longer list, but must be in correct position e.g. $-1, 2, 5$ is B0 |
| | B1 | Obtain all three correct values. Ignore any subsequent values if given |
## Part (ii)
| Answer | Mark | Guidance |
|--------|------|----------|
| $S_{40} = \frac{40}{2}(2 \times 2 + 39 \times 3)$ | B1* | Identify AP with $a = 2$, $d = 3$. Could be stated, listing further terms linked by $+$ sign or by recognisable attempt at any formula for AP including attempt at $u_{40}$ |
| $= 2420$ | M1d* | Attempt to sum first 40 terms of the AP. Must use correct formula with $a = 2$ and $d = 3$. If using $\frac{1}{2}n(a+l)$ then must be valid attempt at $l$. Could use $3\sum n - \sum 1$, but M0 for $3\sum n - 1$ |
| | A1 | Obtain 2420. Either from formula or from manual summing of 40 terms |
---2 A sequence $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by $u _ { n } = 3 n - 1$, for $n \geqslant 1$.\\
(i) Find the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$.\\
(ii) Find $\sum _ { n = 1 } ^ { 40 } u _ { n }$.
\hfill \mbox{\textit{OCR C2 2014 Q2 [5]}}