A geometric series has first term $a$ and common ratio $r$, where $rShow that $27{{r}^{3}}-27{{r}^{2

Question

A geometric series has first term $a$ and common ratio $r$, where $rShow that $27{{r}^{3}}-27{{r}^{2}}+4=0$. [3] Find the values of $r$ and $a$. [1] The $n$ th term of the series is ${{u}_{n}}$. It is given that $80\sum\limits_{r=k+1}^{\infty }{{{u}_{r}}}=\sum\limits_{r=1}^{k}{{{u}_{r}}}$. Find the value of $k$. [3]

Accepted Answer

(a) Shown, (b) $a = 24$, $r = -\frac{1}{3}$, (c) $k = 4$

N2024 P1 Q5

N2024 P1 Q5

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