Question

Find the ratio of a6 and a8 in the G P √32,√16,√8

Answer 1

$\sqrt{32}, \sqrt{16} , \sqrt{8} ,\cdot\cdot\cdot \:are \: in \: G.P$

$First \:term (a) = \sqrt{32}$

$Common \:ratio (r)\\ = \frac{a_{2}}{a_{1}}\\= \frac{\sqrt{16}}{\sqrt{32}}\\= \frac{1}{\sqrt{2}}$

$\boxed { \pink { n^{th}\: term (a_{n}) = a \times r^{n-1} }}$

$a_{6} = a \times r^{6-1} = a r^{5}$

$a_{8} = a \times r^{8-1} = a r^{7}$

$Ratio = \frac{a_{6}}{a_{8}}\\= \frac{a r^{5} }{a r^{7}}\\= \frac{1}{r^{2}}$

$= \frac{1}{\left(\frac{1}{\sqrt{2}}\right)^{2}}\\= \frac{1}{\frac{1}{2}}\\= 2$

Therefore.,

$\red { Ratio \: of \: a_{6} \:and \:a_{8} } \green {= 2}$

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