Answer
General term($n^{th}$ term) = $\frac{3}{2}$$\times$$2^{n}$
Indicated term $a_{10}$ = 1536
Work Step by Step
The given sequence = 3, 6, 12, 24,..........;$a_{10}$
From above we observe $a_{1}$ = 3
common ratio (r) = $\frac{24}{12}$ = $\frac{12}{6}$ = $\frac{6}{3}$ = 2
General term($n^{th}$ term)
= $a_{n}$ = $a_{1}$ $r^{n-1}$
= 3$\times$$2^{n-1}$
= 3$\times$$2^{n}$$\times$$2^{-1}$
= $\frac{3}{2}$$\times$$2^{n}$
Indicated term $a_{10}$ = $\frac{3}{2}$$\times$$2^{10}$= $\frac{3}{2}$$\times$1024 = 3$\times$512 = 1536
