| Exam Board | OCR MEI |
|---|---|
| Module | Paper 1 (Paper 1) |
| Year | 2021 |
| Session | November |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Sequences and Series |
| Type | Periodic Sequences |
| Difficulty | Moderate -0.8 This question tests basic definitions and standard formulas. Part (a) involves recognizing a periodic sequence and summing complete cycles (trivial arithmetic). Part (b) requires stating convergence conditions for geometric sequences and applying the infinite GP formula—both are direct recall with minimal problem-solving. Suitable for early Further Maths students with straightforward, textbook-style parts. |
| Spec | 1.04f Sequence types: increasing, decreasing, periodic1.04g Sigma notation: for sums of series1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Sequence is periodic [with period 4] | B1 [1] | Do not allow "repeating", "recurring" etc. Sequence can also be described as oscillating |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Total of 200 terms is \(50 \times (2+3+0+3) = 400\) | B1 [1] | cao |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Sequence divergent for either \(b > 1\) | B1 | Allow for one correct inequality. Note for \(b=1\) the sequence is convergent, but the corresponding series is divergent |
| or \(b \leq -1\) | B1 [2] | Must have "or" or the union of sets. Condone \(b < -1\) or \( |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Marks | Guidance |
| Infinite sum of geometric series with \(a = \frac{1}{3}\), \(r = \frac{1}{3}\) | M1 | Using the sum of geometric series with \(r = \frac{1}{3}\) |
| \(S = \dfrac{a}{1-r} = \dfrac{\frac{1}{3}}{1 - \frac{1}{3}} = \dfrac{1}{2}\) | A1 [2] | www |
## Question 4(a)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Sequence is periodic [with period 4] | B1 [1] | Do not allow "repeating", "recurring" etc. Sequence can also be described as oscillating |
---
## Question 4(a)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Total of 200 terms is $50 \times (2+3+0+3) = 400$ | B1 [1] | cao |
---
## Question 4(b)(i):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Sequence divergent for either $b > 1$ | B1 | Allow for one correct inequality. Note for $b=1$ the sequence is convergent, but the corresponding series is divergent |
| or $b \leq -1$ | B1 [2] | Must have "or" or the union of sets. Condone $b < -1$ or $|b| > 1$ |
---
## Question 4(b)(ii):
| Answer | Marks | Guidance |
|--------|-------|----------|
| Infinite sum of geometric series with $a = \frac{1}{3}$, $r = \frac{1}{3}$ | M1 | Using the sum of geometric series with $r = \frac{1}{3}$ |
| $S = \dfrac{a}{1-r} = \dfrac{\frac{1}{3}}{1 - \frac{1}{3}} = \dfrac{1}{2}$ | A1 [2] | www |
---4
\begin{enumerate}[label=(\alph*)]
\item The first four terms of a sequence are $2,3,0,3$ and the subsequent terms are given by $\mathrm { a } _ { \mathrm { k } + 4 } = \mathrm { a } _ { \mathrm { k } }$.
\begin{enumerate}[label=(\roman*)]
\item State what type of sequence this is.
\item Find $\sum _ { \mathrm { k } = 1 } ^ { 200 } \mathrm { a } _ { \mathrm { k } }$.
\end{enumerate}\item A different sequence is given by $\mathrm { u } _ { \mathrm { n } } = \mathrm { b } ^ { \mathrm { n } }$ where $b$ is a constant and $n \geqslant 1$.
\begin{enumerate}[label=(\roman*)]
\item State the set of values of $b$ for which this is a divergent sequence.
\item In the case where $b = \frac { 1 } { 3 }$, find the sum of all the terms in the sequence.
\end{enumerate}\end{enumerate}
\hfill \mbox{\textit{OCR MEI Paper 1 2021 Q4 [6]}}