| Exam Board | OCR MEI |
|---|---|
| Module | Paper 2 (Paper 2) |
| Year | 2024 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Arithmetic Sequences and Series |
| Type | Sigma notation: arithmetic series evaluation |
| Difficulty | Easy -1.3 This is a straightforward arithmetic sequence question requiring only basic recall and application of standard formulas. Part (a) involves simple addition, (b) is definitional knowledge, (c) uses the direct formula u_n = u_1 + (n-1)d, and (d) applies the standard sum formula. No problem-solving insight or novel reasoning is required—purely mechanical application of well-rehearsed techniques. |
| Spec | 1.04e Sequences: nth term and recurrence relations1.04f Sequence types: increasing, decreasing, periodic1.04h Arithmetic sequences: nth term and sum formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(u_2 = 3, u_3 = 8, u_4 = 13\) | B1 | B0 if wrongly attributed |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Divergent because difference between consecutive terms is not decreasing | E1 | Allow: divergent because ratio of consecutive terms is tending to 1 not 0; terms not tending to a finite limit oe; terms tend to infinity oe. Do not allow: divergent because not convergent; terms increase infinitely; terms get bigger |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(u_{30} = -2 + (30-1) \times 5\) used oe | M1 | \(a\) must be \(u_0, u_1, u_2, u_3\) or \(u_4\); \(d\) must be 5; must see at least \(-2 + 29 \times 5\) |
| \(143\) | A1 | If M0 allow SCB1 for 143 not fully supported |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| \(S_{30} = \frac{30}{2}(-2 + \text{their } 143)\) oe or \(S_{30} = \frac{30}{2}(2 \times (-2) + (30-1) \times 5)\) oe | M1 | \(a\) must be \(-2\) and \(d\) must be 5; must see at least \(15 \times (-2 + \text{their } 143)\) or \(15 \times (-4 + 29 \times 5)\) |
| \(2115\) | A1 | If M0 allow SCB1 for 2115 not fully supported |
## Question 7:
### Part (a):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $u_2 = 3, u_3 = 8, u_4 = 13$ | B1 | B0 if wrongly attributed |
### Part (b):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Divergent because difference between consecutive terms is not decreasing | E1 | Allow: divergent because ratio of consecutive terms is tending to 1 not 0; terms not tending to a finite limit oe; terms tend to infinity oe. Do **not** allow: divergent because not convergent; terms increase infinitely; terms get bigger |
### Part (c):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $u_{30} = -2 + (30-1) \times 5$ used oe | M1 | $a$ must be $u_0, u_1, u_2, u_3$ or $u_4$; $d$ must be 5; must see at least $-2 + 29 \times 5$ |
| $143$ | A1 | If M0 allow SCB1 for 143 not fully supported |
### Part (d):
| Answer | Marks | Guidance |
|--------|-------|----------|
| $S_{30} = \frac{30}{2}(-2 + \text{their } 143)$ oe **or** $S_{30} = \frac{30}{2}(2 \times (-2) + (30-1) \times 5)$ oe | M1 | $a$ must be $-2$ and $d$ must be 5; must see at least $15 \times (-2 + \text{their } 143)$ or $15 \times (-4 + 29 \times 5)$ |
| $2115$ | A1 | If M0 allow SCB1 for 2115 not fully supported |
---7 A sequence is defined by the recurrence relation $\mathrm { u } _ { \mathrm { k } + 1 } = \mathrm { u } _ { \mathrm { k } } + 5$ with $\mathrm { u } _ { 1 } = - 2$.
\begin{enumerate}[label=(\alph*)]
\item Write down the values of $u _ { 2 } , u _ { 3 }$, and $u _ { 4 }$.
\item Explain whether this sequence is divergent or convergent.
\item Determine the value of $u _ { 30 }$.
\item Determine the value of $\sum _ { \mathrm { k } = 1 } ^ { 30 } \mathrm { u } _ { \mathrm { k } }$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 2 2024 Q7 [6]}}