| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2011 |
| Session | January |
| Marks | 6 |
| 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 C2 question requiring direct substitution into a linear formula, recognition of an arithmetic sequence, and application of the standard sum formula. All parts are routine with no problem-solving required—significantly easier than average A-level questions. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04g Sigma notation: for sums of series1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Obtain at least one correct term | B1 | Just a list of numbers is fine, no need for labels. |
| Obtain all three correct terms | B1 (2) | Ignore extra terms beyond \(u_3\). |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Arithmetic progression | B1 (1) | Allow AP, but not description e.g. constant difference. Ignore extra description as long as not wrong or contradictory. |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| Attempt relevant \(S_n\) using correct formula | M1 | Must use correct formula to sum an AP. Must use \(d=3\). Must be finding sum of 99, 100, 101 or 200 terms with \(a\) consistent with their \(n\). |
| Attempt correct method to find required sum | M1 | Need to show subtraction. Still need \(a=5\) and \(d=3\). \(S_{200} - S_{101}\) is M0. |
| Obtain \(45{,}350\) | A1 (3) | Answer only gets full marks. SR: M1 attempt to sum all terms from \(u_{101}\) to \(u_{200}\); A2 obtain \(45{,}350\). |
# Question 2:
## Part (i): $u_1 = 5,\ u_2 = 8,\ u_3 = 11$
| Answer/Working | Mark | Guidance |
|---|---|---|
| Obtain at least one correct term | B1 | Just a list of numbers is fine, no need for labels. |
| Obtain all three correct terms | B1 (2) | Ignore extra terms beyond $u_3$. |
## Part (ii): Arithmetic progression
| Answer/Working | Mark | Guidance |
|---|---|---|
| Arithmetic progression | B1 (1) | Allow AP, but not description e.g. constant difference. Ignore extra description as long as not wrong or contradictory. |
## Part (iii): $S = \frac{100}{2}(305 + 602)$ or $\frac{100}{2}(2\times305 + 99\times3) = 45{,}350$
| Answer/Working | Mark | Guidance |
|---|---|---|
| Attempt relevant $S_n$ using correct formula | M1 | Must use correct formula to sum an AP. Must use $d=3$. Must be finding sum of 99, 100, 101 or 200 terms with $a$ consistent with their $n$. |
| Attempt correct method to find required sum | M1 | Need to show subtraction. Still need $a=5$ and $d=3$. $S_{200} - S_{101}$ is M0. |
| Obtain $45{,}350$ | A1 (3) | Answer only gets full marks. **SR:** M1 attempt to sum all terms from $u_{101}$ to $u_{200}$; A2 obtain $45{,}350$. |
---2 A sequence $S$ has terms $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ defined by $u _ { n } = 3 n + 2$ for $n \geqslant 1$.\\
(i) Write down the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$.\\
(ii) State what type of sequence $S$ is.\\
(iii) Find $\sum _ { n = 101 } ^ { 200 } u _ { n }$.
\hfill \mbox{\textit{OCR C2 2011 Q2 [6]}}