OCR MEI C2 2007 January — Question 8 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicArithmetic Sequences and Series
TypeFind term or common difference
DifficultyModerate -0.3 This is a straightforward two-equation system using standard AP formulas (a + 6d = 6 and 10a + 45d = 30). It requires routine algebraic manipulation with no conceptual difficulty, making it slightly easier than average but still requiring proper method.
Spec1.04h Arithmetic sequences: nth term and sum formulae1.04i Geometric sequences: nth term and finite series sum
8 The 7th term of an arithmetic progression is 6. The sum of the first 10 terms of the progression is 30. Find the 5th term of the progression.
Question 8:
AnswerMarks Guidance
\(a + 6d = 6\)B1 7th term
\(\frac{10}{2}(2a + 9d) = 30\), so \(2a + 9d = 6\)B1 Sum formula
Solving: \(2(6 - 6d) + 9d = 6 \Rightarrow 12 - 12d + 9d = 6\)M1 Eliminating one variable
\(d = 2\), \(a = 6 - 12 = -6\)A1 Both values
5th term \(= a + 4d = -6 + 8 = 2\)A1 cao 
## Question 8:
$a + 6d = 6$ | B1 | 7th term
$\frac{10}{2}(2a + 9d) = 30$, so $2a + 9d = 6$ | B1 | Sum formula
Solving: $2(6 - 6d) + 9d = 6 \Rightarrow 12 - 12d + 9d = 6$ | M1 | Eliminating one variable
$d = 2$, $a = 6 - 12 = -6$ | A1 | Both values
5th term $= a + 4d = -6 + 8 = 2$ | A1 | cao

---
8 The 7th term of an arithmetic progression is 6. The sum of the first 10 terms of the progression is 30.

Find the 5th term of the progression.

\hfill \mbox{\textit{OCR MEI C2 2007 Q8 [5]}}
This paper (13 questions)
View full paper
Q1 2 Q2 3 Q3 3 Q4 3 Q5 5 Q6 4 Q7 3 Q8 5 Q9 4 Q10 4 Q11 12 Q12 12 Q13 12