OCR MEI C2 2007 January — Question 2 3 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2007
SessionJanuary
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeFind sum to infinity
DifficultyModerate -0.8 This is a straightforward application of the sum to infinity formula S∞ = a/(1-r). Given a=6 and S∞=5, students simply substitute and solve 5 = 6/(1-r) to find r=1/5. It requires only direct recall of a standard formula with minimal algebraic manipulation, making it easier than average but not trivial since students must recognize which formula to use and handle the algebra correctly.
Spec1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1
2 A geometric progression has 6 as its first term. Its sum to infinity is 5 .
Calculate its common ratio.
Question 2:
AnswerMarks Guidance
\(S_\infty = \frac{a}{1-r}\) so \(5 = \frac{6}{1-r}\)M1 Correct formula used
\(1 - r = \frac{6}{5}\), \(r = -\frac{1}{5}\)A1 A1 cao 
## Question 2:
$S_\infty = \frac{a}{1-r}$ so $5 = \frac{6}{1-r}$ | M1 | Correct formula used
$1 - r = \frac{6}{5}$, $r = -\frac{1}{5}$ | A1 A1 | cao

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2 A geometric progression has 6 as its first term. Its sum to infinity is 5 .\\
Calculate its common ratio.

\hfill \mbox{\textit{OCR MEI C2 2007 Q2 [3]}}
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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