Question 6 - A-Level Maths

OCR C2 2008 January — Question 6 8 marks

Exam Board	OCR
Module	C2 (Core Mathematics 2)
Year	2008
Session	January
Marks	8
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 into a given formula, recognition of sequence type, and application of the standard sum formula. All steps are routine with no problem-solving insight needed, making it easier than average for A-level.
Spec	1.04h Arithmetic sequences: nth term and sum formulae

6 A sequence of terms $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by $$u _ { n } = 2 n + 5 , \quad \text { for } n \geqslant 1 .$$

Write down the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$.
State what type of sequence it is.
Given that $\sum _ { n = 1 } ^ { N } u _ { n } = 2200$, find the value of $N$.

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Question 6:

Part (i)

Answer	Marks	Guidance
$u_1 = 7$, $u_2 = 9$, $u_3 = 11$	B1, B1 [2]	Correct $u_1$; Correct $u_2$ and $u_3$

Part (ii)

Answer	Marks	Guidance
Arithmetic Progression	B1 [1]	Any mention of arithmetic

Part (iii)

Answer	Marks	Guidance
$\frac{1}{2}N(14 + (N-1) \times 2) = 2200$	B1, M1	Correct interpretation of sigma notation; Attempt sum of AP and equate to 2200
$N^2 + 6N - 2200 = 0$	A1	Correct (unsimplified) equation
$(N-44)(N+50) = 0$	M1	Attempt to solve 3 term quadratic in $N$
hence $N = 44$	A1 [5]	Obtain $N = 44$ only ($N = 44$ www is full marks)

# Question 6:

## Part (i)
| $u_1 = 7$, $u_2 = 9$, $u_3 = 11$ | B1, B1 **[2]** | Correct $u_1$; Correct $u_2$ and $u_3$ |

## Part (ii)
| Arithmetic Progression | B1 **[1]** | Any mention of arithmetic |

## Part (iii)
| $\frac{1}{2}N(14 + (N-1) \times 2) = 2200$ | B1, M1 | Correct interpretation of sigma notation; Attempt sum of AP and equate to 2200 |
| $N^2 + 6N - 2200 = 0$ | A1 | Correct (unsimplified) equation |
| $(N-44)(N+50) = 0$ | M1 | Attempt to solve 3 term quadratic in $N$ |
| hence $N = 44$ | A1 **[5]** | Obtain $N = 44$ only ($N = 44$ www is full marks) |

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Show LaTeX source

6 A sequence of terms $u _ { 1 } , u _ { 2 } , u _ { 3 } , \ldots$ is defined by

$$u _ { n } = 2 n + 5 , \quad \text { for } n \geqslant 1 .$$

(i) Write down the values of $u _ { 1 } , u _ { 2 }$ and $u _ { 3 }$.\\
(ii) State what type of sequence it is.\\
(iii) Given that $\sum _ { n = 1 } ^ { N } u _ { n } = 2200$, find the value of $N$.

\hfill \mbox{\textit{OCR C2 2008 Q6 [8]}}

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Q1 4 Q2 4 Q3 4 Q4 5 Q5 6 Q6 8 Q7 8 Q8 11 Q9 9 Q10 12

Answer	Marks	Guidance
\(\frac{1}{2}N(14 + (N-1) \times 2) = 2200\)	B1, M1	Correct interpretation of sigma notation; Attempt sum of AP and equate to 2200
\(N^2 + 6N - 2200 = 0\)	A1	Correct (unsimplified) equation
\((N-44)(N+50) = 0\)	M1	Attempt to solve 3 term quadratic in \(N\)
hence \(N = 44\)	A1 [5]	Obtain \(N = 44\) only (\(N = 44\) www is full marks)