Question 2 - A-Level Maths

OCR MEI C2 — Question 2 5 marks

Exam Board	OCR MEI
Module	C2 (Core Mathematics 2)
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 to find terms, recognition of sequence type, and application of the standard arithmetic series formula. All steps are routine with no problem-solving or novel insight needed.
Spec	1.04e Sequences: nth term and recurrence relations 1.04g Sigma notation: for sums of series 1.04h Arithmetic sequences: nth term and sum formulae

2 The $n$th term of a sequence, $u _ { n }$, is given by $$u _ { n } = 12 - \frac { 1 } { 2 } n .$$

Write down the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$. State what type of sequence this is.
Find $\sum _ { n = 1 } ^ { 30 } u _ { n }$.

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Question 2(i):

Answer	Marks	Guidance
11.5, 11 and 10.5 oe	B1	ignore labelling
Arithmetic and/or divergent	B1	allow AP; ignore references to $a$, $d$ or $n$; incorrect embellishments such as converging arithmetic, diverging geometric do not score. B0 if a choice is given e.g. AP/GP

Question 2(ii):

Answer	Marks	Guidance
$n = 30$ identified as number of terms in relevant AP	B1	e.g. $1+2+3+...+30$ is not a relevant AP
$S_{30} = \frac{30}{2}(2 \times 11.5 + (30-1) \times -0.5)$	M1	or $S_{30} = \frac{30}{2}(11.5 + -3)$; condone one error in $a$, $d$ or $n$ but do not condone $l = -\frac{1}{2}$
127.5 oe	A1	allow recovery from slip in working (e.g. omission of minus sign); SC3 if each term calculated and summed to correct answer or for 127.5 unsupported

## Question 2(i):
| 11.5, 11 and 10.5 oe | B1 | ignore labelling |
| Arithmetic and/or divergent | B1 | allow AP; ignore references to $a$, $d$ or $n$; incorrect embellishments such as converging arithmetic, diverging geometric do not score. **B0** if a choice is given e.g. AP/GP |

## Question 2(ii):
| $n = 30$ identified as number of terms in relevant AP | B1 | e.g. $1+2+3+...+30$ is not a relevant AP |
| $S_{30} = \frac{30}{2}(2 \times 11.5 + (30-1) \times -0.5)$ | M1 | or $S_{30} = \frac{30}{2}(11.5 + -3)$; condone one error in $a$, $d$ or $n$ but do not condone $l = -\frac{1}{2}$ |
| 127.5 oe | A1 | allow recovery from slip in working (e.g. omission of minus sign); **SC3** if each term calculated and summed to correct answer or for 127.5 unsupported |

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2 The $n$th term of a sequence, $u _ { n }$, is given by

$$u _ { n } = 12 - \frac { 1 } { 2 } n .$$

(i) Write down the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$. State what type of sequence this is.\\
(ii) Find $\sum _ { n = 1 } ^ { 30 } u _ { n }$.

\hfill \mbox{\textit{OCR MEI C2  Q2 [5]}}

This paper (12 questions)

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Q1 3 Q2 5 Q3 3 Q4 2 Q5 13 Q6 2 Q7 4 Q8 3 Q9 4 Q10 3 Q11 2 Q12 5

Answer	Marks	Guidance
\(n = 30\) identified as number of terms in relevant AP	B1	e.g. \(1+2+3+...+30\) is not a relevant AP
\(S_{30} = \frac{30}{2}(2 \times 11.5 + (30-1) \times -0.5)\)	M1	or \(S_{30} = \frac{30}{2}(11.5 + -3)\); condone one error in \(a\), \(d\) or \(n\) but do not condone \(l = -\frac{1}{2}\)
127.5 oe	A1	allow recovery from slip in working (e.g. omission of minus sign); SC3 if each term calculated and summed to correct answer or for 127.5 unsupported