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

Common ratio = $\dfrac{6}{2}$ = 3.

Let n be no. of terms taken.

Since, r > 1

$\Rightarrow S = \dfrac{a(r^n - 1)}{(r - 1)} \\[1em] \Rightarrow 728 = \dfrac{2 \times (3^n - 1)}{3 - 1} \\[1em] \Rightarrow 728 = \dfrac{2(3^n - 1)}{2} \\[1em] \Rightarrow 3^n - 1 = 728 \\[1em] \Rightarrow 3^n = 729 \\[1em] \Rightarrow 3^n = 3^6 \\[1em] \Rightarrow n = 6.$

Hence, 6 terms must be taken to make the sum equal to 728.