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Q.
A geometric sequence has four positive terms $a_1, a_2, a_3, a_4$. If $\frac{a_3}{a_1}=9$ and $a_1+a_2=\frac{4}{3}$, then $a_4$ equals
Sequences and Series
Solution:
$\frac{ ar ^2}{ a }=9 \Rightarrow r =3$
$a+a r=\frac{4}{3} \therefore a \cdot 4=\frac{4}{3} \Rightarrow a=\frac{1}{3}$
$\therefore a_4= ar ^3=\frac{1}{3} \cdot 3^3=3^2=9$