How many terms of the series 2 + 6 + 18 + ... must be taken to make the sum equal to 728?

Here, a = 2

Common ratio, r = 3

Sum of n terms, Sn = 728

$S_{n}=2\left(\frac{3^{n}-1}{3-1}\right)$

$\Rightarrow 728=2\left(\frac{3^{n}-1}{2}\right)$

$\Rightarrow 728=3^{n}-1$

$\Rightarrow 3^{n}=729$

$\Rightarrow 3^{n}=3^{6}$

$\therefore n=6$