OCR MEI C2 2005 January — Question 5 5 marks

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2005
SessionJanuary
Marks5
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeFind sum to infinity
DifficultyModerate -0.8 This is a straightforward geometric progression question requiring only direct application of standard formulas. Students identify r = 1/2, apply the nth term formula to get 4(1/2)^19 = 2^-17, and use the sum to infinity formula S = a/(1-r) = 8. Both parts are routine calculations with no problem-solving or conceptual challenges beyond basic GP knowledge.
Spec1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1
5 The first three terms of a geometric progression are 4, 2, 1.
Find the twentieth term, expressing your answer as a power of 2.
Find also the sum to infinity of this progression.
AnswerMarks Guidance
\(a = 4, r = \frac{1}{2}\) identifiedB1 Stated or identified by correct use
\(2^{-17}\)T2 M1 20th term = their\((a)×\)(their \(r)^{19}\)
\(8\)S2 M1 \(S = \) their \((a) / (1-\)their \((r))\)
5 marks 
$a = 4, r = \frac{1}{2}$ identified | B1 | Stated or identified by correct use
$2^{-17}$ | T2 | M1 20th term = their$(a)×$(their $r)^{19}$
$8$ | S2 | M1 $S = $ their $(a) / (1-$their $(r))$
| | 5 marks |
5 The first three terms of a geometric progression are 4, 2, 1.\\
Find the twentieth term, expressing your answer as a power of 2.\\
Find also the sum to infinity of this progression.

\hfill \mbox{\textit{OCR MEI C2 2005 Q5 [5]}}
This paper (11 questions)
View full paper
Q1 3 Q2 4 Q3 4 Q4 5 Q5 5 Q6 5 Q7 5 Q8 5 Q9 12 Q10 11 Q11 13