OCR MEI C2 — Question 5 3 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Marks3
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Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeNew GP from transformation
DifficultyModerate -0.8 This question tests basic manipulation of the geometric series sum formula S = a/(1-r). Part (i) is immediate substitution (answer: 2S), and part (ii) requires one algebraic step to simplify a/(1-r²) in terms of S. Both parts are routine applications with no problem-solving required, making this easier than average for A-level.
Spec1.04j Sum to infinity: convergent geometric series |r|<1
\(S\) is the sum to infinity of a geometric progression with first term \(a\) and common ratio \(r\).
  1. Another geometric progression has first term \(2a\) and common ratio \(r\). Express the sum to infinity of this progression in terms of \(S\). [1]
  2. A third geometric progression has first term \(a\) and common ratio \(r^2\). Express, in its simplest form, the sum to infinity of this progression in terms of \(S\) and \(r\). [2]
Question 5:
AnswerMarks Guidance
5(i) 2S cao
[1]
AnswerMarks Guidance
5(ii) a
1r2
S 1
or S
AnswerMarks
1r 1rM1
A1
AnswerMarks
[2]1r
if M0, SC1 for Soe
1r2
Question 5:
5 | (i) | 2S cao | B1
[1]
5 | (ii) | a
1r2
S 1
or S
1r 1r | M1
A1
[2] | 1r
if M0, SC1 for Soe
1r2
$S$ is the sum to infinity of a geometric progression with first term $a$ and common ratio $r$.

\begin{enumerate}[label=(\roman*)]
\item Another geometric progression has first term $2a$ and common ratio $r$. Express the sum to infinity of this progression in terms of $S$. [1]
\item A third geometric progression has first term $a$ and common ratio $r^2$. Express, in its simplest form, the sum to infinity of this progression in terms of $S$ and $r$. [2]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI C2  Q5 [3]}}
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Q1 5 Q2 12 Q3 5 Q4 5 Q5 3 Q6 4 Q7 10