Question

Please answer it .......... I need method

Answer 1

Solution:

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Given:

In a G.P.

$T_2 = 2 \sqrt{2}$

&

$T_9 = 32$

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To find:

 value of common ratio (r)

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We know that ,

$T_n = ar^{n-1}$

So,

=> $T_2 = ar^{2-1} = ar$

&

=> $T_9 = ar^{9-1} = ar^8$


So,

 => $ar = 2 \sqrt{2}$
 
 => $ar^8 = 32$

=> $\frac{ar^8}{ar} = r^7$

=> $\frac{32}{2 \sqrt{2} } = 8 \sqrt{2}$

So,

=> $r^7 = 8 \sqrt{2}$

=> $r^7 = (2)^{3} ( \sqrt{2}) =( ( \sqrt{2} )^2)^3 ( \sqrt{2} ) = (\sqrt{2})^6 (\sqrt{2}) = ( \sqrt{2})^7$

So,

=> $r^7 = (\sqrt{2})^7$

=> r = $\sqrt{2}$

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                                               Hope it Helps !!