A non-zero sequence $\{{{u}_{n}}\}$ where $n\ge 1$ and ${{u}_{i}}
e {{u}_{j}}$ when $i
e j$ is suc

Question

A non-zero sequence $\{{{u}_{n}}\}$ where $n\ge 1$ and ${{u}_{i}}
e {{u}_{j}}$ when $i
e j$ is such that $\frac{1}{{{u}_{n+1}}-{{u}_{n}}}$, $\frac{1}{2{{u}_{n+1}}}$, $\frac{1}{{{u}_{n+1}}-{{u}_{n+2}}}$ are consecutive terms of an arithmetic progression. Show that $\{{{u}_{n}}\}$ forms a geometric progression. [3] A geometric series has first term $1$ and common ratio $r$, where $0 [5]

Accepted Answer

(a) $\{u_n\}$ is a geometric progression (b) $r^{12}=\frac12(\sqrt3-1)$

2022 HCI J1 BT Q5

2022 HCI J1 BT Q5

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