CAIE P1 2022 November — Question 4 4 marks

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2022
SessionNovember
Marks4
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicGeometric Sequences and Series
TypeFind specific nth term
DifficultyStandard +0.3 This is a straightforward geometric progression problem requiring students to set up two equations from given information (ar² = 1764 and ar + ar² = 3444), solve for a and r, then calculate ar⁴⁹. While it involves multiple steps and algebraic manipulation, it follows a standard template that students practice extensively, making it slightly easier than average.
Spec1.04i Geometric sequences: nth term and finite series sum
4 A geometric progression is such that the third term is 1764 and the sum of the second and third terms is 3444 . Find the 50th term.
Question 4:
AnswerMarks Guidance
AnswerMark Guidance
\(ar^2 = 1764\) and \(ar + ar^2 = 3444\) or \(ar = 1680\) or \(\frac{a(1-r^3)}{1-r} - a = 3444\)B1 Two correct algebraic statements.
Attempt to solve as far as \(r =\) or \(a =\)M1 Any valid method, e.g. \(1764 \div 1680\) or from \(20r^2 - 41r + 21\) OE (condone solving using a calculator).
\(r = \frac{1764}{1680} = \frac{21}{20}\) or \(1.05\ [a = 1600]\)A1 Note: \(r = \frac{1764}{3444 - 1764}\) www implies B1 and M1.
\(17\ 500\)A1 AWRT e.g. \(17\ 474.1\)… 
## Question 4:

| Answer | Mark | Guidance |
|--------|------|----------|
| $ar^2 = 1764$ and $ar + ar^2 = 3444$ or $ar = 1680$ or $\frac{a(1-r^3)}{1-r} - a = 3444$ | B1 | Two correct algebraic statements. |
| Attempt to solve as far as $r =$ or $a =$ | M1 | Any valid method, e.g. $1764 \div 1680$ or from $20r^2 - 41r + 21$ OE (condone solving using a calculator). |
| $r = \frac{1764}{1680} = \frac{21}{20}$ or $1.05\ [a = 1600]$ | A1 | Note: $r = \frac{1764}{3444 - 1764}$ www implies B1 and M1. |
| $17\ 500$ | A1 | AWRT e.g. $17\ 474.1$… |

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4 A geometric progression is such that the third term is 1764 and the sum of the second and third terms is 3444 .

Find the 50th term.\\

\hfill \mbox{\textit{CAIE P1 2022 Q4 [4]}}
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