| Exam Board | OCR |
|---|---|
| Module | C2 (Core Mathematics 2) |
| Year | 2005 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sequence defined by formula |
| Difficulty | Easy -1.3 This is a straightforward arithmetic sequence question requiring only direct substitution to find terms and application of the standard sum formula. Part (i) is trivial arithmetic, and part (ii) is a routine application of the arithmetic series formula with no problem-solving required—significantly easier than average A-level questions. |
| Spec | 1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (i) \(u_1 = 2, u_2 = 5, u_3 = 8\) | B1, B1, B1 | For the correct value of \(u_1\); For both correct values of \(u_2\) and \(u_3\); For a correct statement (any mention of arithmetic) |
| The sequence is an Arithmetic Progression | B1 | |
| (ii) \(\frac{1}{2} \times 100 \times (2 \times 2 + 99 \times 3) = 15050\) | M1, M1, A1 | For correct interpretation of Sigma notation – ie finding the sum of an AP or GP; For use of correct \(\frac{1}{2}n(2a + (n-1)d)\), or equiv, with \(n=100\) and \(a\) & \(d\) not both =1; For correct value 15050 |
**(i)** $u_1 = 2, u_2 = 5, u_3 = 8$ | B1, B1, B1 | For the correct value of $u_1$; For both correct values of $u_2$ and $u_3$; For a correct statement (any mention of arithmetic)
The sequence is an Arithmetic Progression | B1 |
**(ii)** $\frac{1}{2} \times 100 \times (2 \times 2 + 99 \times 3) = 15050$ | M1, M1, A1 | For correct interpretation of Sigma notation – ie finding the sum of an AP or GP; For use of correct $\frac{1}{2}n(2a + (n-1)d)$, or equiv, with $n=100$ and $a$ & $d$ not both =1; For correct value 15050
---1 A sequence $S$ has terms $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ defined by
$$u _ { n } = 3 n - 1 ,$$
for $n \geqslant 1$.\\
(i) Write down the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$, and state what type of sequence $S$ is.\\
(ii) Evaluate $\sum _ { n = 1 } ^ { 100 } u _ { n }$.
\hfill \mbox{\textit{OCR C2 2005 Q1 [6]}}