CAIE P1 2022 June — Question 2 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJune
Marks4
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Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeFind sum to infinity
DifficultyModerate -0.5 This is a straightforward application of standard geometric series formulas: find the common ratio from consecutive terms (r = 8/10 = 0.8), then the first term (a = 10/0.8 = 12.5), and finally apply S_∞ = a/(1-r). It requires only routine recall and basic algebra with no problem-solving insight, making it slightly easier than average.
Spec1.04i Geometric sequences: nth term and finite series sum1.04j Sum to infinity: convergent geometric series |r|<1
2 The second and third terms of a geometric progression are 10 and 8 respectively.
Find the sum to infinity.
Question 2:
AnswerMarks Guidance
AnswerMark Guidance
\(r = 0.8\)B1 OE
\(a = 12.5\)B1 OE
\(S_{\infty} = 12.5 \div (1 - 0.8)\)M1 Using \(\frac{a}{1-r}\) with 'their \(a\)' and 'their \(r\)' but \(
\(S_{\infty} = \frac{125}{2}\), \(62\frac{1}{2}\) or \(62.5\)A1 \(\frac{12\frac{1}{2}}{\frac{1}{5}}\) or similar does not get A1.
Total: 4 
## Question 2:

| Answer | Mark | Guidance |
|--------|------|----------|
| $r = 0.8$ | B1 | OE |
| $a = 12.5$ | B1 | OE |
| $S_{\infty} = 12.5 \div (1 - 0.8)$ | M1 | Using $\frac{a}{1-r}$ with 'their $a$' and 'their $r$' but $|r|$ must be $< 1$. |
| $S_{\infty} = \frac{125}{2}$, $62\frac{1}{2}$ or $62.5$ | A1 | $\frac{12\frac{1}{2}}{\frac{1}{5}}$ or similar **does not** get A1. |
| **Total: 4** | | |
2 The second and third terms of a geometric progression are 10 and 8 respectively.\\
Find the sum to infinity.\\

\hfill \mbox{\textit{CAIE P1 2022 Q2 [4]}}
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