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  4. Let 9 GM's are inserted between 100 and 3200 . Then number of rational GM's are

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Q. Let $9 \,GM's $ are inserted between $100$ and $3200 $ . Then number of rational GM's are

Sequences and Series

Solution:

$3200=100 r ^{10}$
$ \Rightarrow r =\pm \sqrt{2}$
Consider $r =2^{\frac{1}{2}}$
$\Rightarrow G _{1}=100 r =100 \sqrt{2} $ (not rational)
$\Rightarrow G _{2}, G _{4}, G _{6}, G _{8}$ are rational terms