Jambmaths question:
If the 2nd term of a G.P is $\tfrac{8}{9}$ and the 6th term is$4\tfrac{1}{2}$. Find the common ratio
Option A:
2
Option B:
$\tfrac{3}{2}$
Option C:
$\tfrac{2}{3}$
Option D:
3
Jamb Maths Solution:
$\begin{align} & {{T}_{n}}=a{{r}^{n-1}} \\ & {{T}_{2}}=a{{r}^{2-1}}=ar=\tfrac{8}{9} \\ & {{T}_{6}}=a{{r}^{6-1}}=a{{r}^{5}}=\tfrac{9}{2} \\ & \frac{{{T}_{6}}}{{{T}_{2}}}=\frac{a{{r}^{5}}}{ar}=\frac{\tfrac{9}{2}}{\tfrac{8}{9}} \\ & {{a}^{4}}=\frac{81}{16} \\ & a=\sqrt[4]{\frac{81}{16}}=\frac{3}{2} \\\end{align}$
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