The ${2^{\mathrm{nd}}}$, ${3^{\mathrm{rd}}}$ and ${4^{\mathrm{th}}}$ terms of a geometric progression are ${\cos\theta}$, ${\sqrt{2}\sin\theta}$ and ${\sqrt{3}\tan\theta}$, respectively, where&nbsp;${0&lt;\theta&lt;\frac{\pi}{2}}$.
Show clearly that the sum of the first ${6}$ terms of the progression is
${\frac{43}{12}\left(6+\sqrt{6}\right)}$.

The ${2^{\mathrm{nd}}}$, ${3^{\mathrm{rd}}}$ and ${4^{\mathrm{th}}}$ terms of a geometric progression are ${\cos\theta}$, ${\sqrt{2}\sin\theta}$ and ${\sqrt{3}\tan\theta}$, respectively, where ${0<\theta<\frac{\pi}{2}}$.

Show clearly that the sum of the first ${6}$ terms of the progression is

${\frac{43}{12}\left(6+\sqrt{6}\right)}$.

Geometric Progression

Sequence and Series

International Baccalaureate Mathematics: Analysis and Approaches Higher Level

Sequence and Series - Geometric Progression

Sequence and Series - Geometric Progression

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