CAIE P1 2021 June — Question 5 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeForm and solve quadratic in parameter
DifficultyStandard +0.3 This is a straightforward geometric progression problem requiring students to use the relationship between consecutive terms to form equations, solve a quadratic for k, find the common ratio, and apply the sum to infinity formula. While it involves multiple steps, each is standard and the path is clear once the GP property (ratio between consecutive terms is constant) is applied.
Spec1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1
5 The fifth, sixth and seventh terms of a geometric progression are \(8 k , - 12\) and \(2 k\) respectively. Given that \(k\) is negative, find the sum to infinity of the progression.
Question 5:
AnswerMarks Guidance
AnswerMarks Guidance
\((-12)^2 = 8k \times 2k\)M1 Forming an equation in \(k\)
\(k = -3\)A1
Using correct formula for \(S_\infty\) \([r = 0.5,\ a = -384]\)M1 With \(-1 < r < 1\)
\(S_\infty = -768\)A1
Alternative method:
\(r^2 = \dfrac{2k}{8k}\)M1
\(r = [\pm]0.5\)A1
Using correct formula for \(S_\infty\) \([r = 0.5,\ a = -384]\)M1 \(-1 < r < 1\)
\(S_\infty = -768\)A1
4 
## Question 5:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $(-12)^2 = 8k \times 2k$ | M1 | Forming an equation in $k$ |
| $k = -3$ | A1 | |
| Using correct formula for $S_\infty$ $[r = 0.5,\ a = -384]$ | M1 | With $-1 < r < 1$ |
| $S_\infty = -768$ | A1 | |
| **Alternative method:** | | |
| $r^2 = \dfrac{2k}{8k}$ | M1 | |
| $r = [\pm]0.5$ | A1 | |
| Using correct formula for $S_\infty$ $[r = 0.5,\ a = -384]$ | M1 | $-1 < r < 1$ |
| $S_\infty = -768$ | A1 | |
| | **4** | |
5 The fifth, sixth and seventh terms of a geometric progression are $8 k , - 12$ and $2 k$ respectively. Given that $k$ is negative, find the sum to infinity of the progression.\\

\hfill \mbox{\textit{CAIE P1 2021 Q5 [4]}}
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