Question

in g.p. (T5\T3)÷(T5×T3)=16:(T1)*2 find r​

Answer 1

$( \frac{ t_{5} }{ t_{3} } ) \div ( t_{5})( t_{3}) = \frac{16}{ { (t_{1} )}^{2} } \\ ( \frac{ t_{5} }{ t_{3} } ) \times \frac{1}{( t_{5})( t_{3})} = \frac{16}{ { (t_{1} )}^{2} } \\ \frac{1}{ { (t_{3} )}^{2} } = \frac{16}{ { (t_{1} )}^{2} } \\ \\ taking \: square \: roots \: on \: both \: sides \\ \\ \frac{1}{ t_{3} } = \frac{4}{ t_{1} } \\ \frac{ t_{1} }{ t_{3}} = 4 \\ \frac{ t_{1} }{ t_{1} {r}^{2} } = 4 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: ... \: ( t_{n} = t_{1} {r}^{n - 1} ) \\ \frac{1}{ {r}^{2} } = 4 \\ {r}^{2} = \frac{1}{2} \\ \\ taking \: square \: root s \: both \: sides$

$\\ \\ r = ±\frac{1}{2}$

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