Question

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

Answer 1

Here, a = 2
Common ratio, r = 3
Sum of n terms, S_n = 728
$$\begin{gathered} S_n=2\left(\frac{3^n-1}{3-1}\right) \\ \Rightarrow 728=2\left(\frac{3^n-1}{2}\right) \\ \Rightarrow 728=3^n-1 \\ \Rightarrow 3^n=729 \\ \Rightarrow 3^n=3^6 \\ \therefore n=6 \end{gathered}$$