Determine the $12^{th}$ term of a G.P whose $8^{th}$ term is 192 and common ratio is 2. Also find $t_8 : t_{12}$
$8^{th}$ term of G.P $= t_8 = ar^7 = 192$
Common ratio $= r = 2$
$\therefore$ $a \times 2^7 = 192$
i.e. $a = \dfrac{192}{128} = \dfrac{3}{2}$
$\therefore$ $12^{th}$ term $= t_{12} = ar^{11} = \dfrac{3}{2} \times 2^{11} = 3072$
$\dfrac{t_8}{t_{12}} = \dfrac{192}{3072} = \dfrac{1}{16}$