Question

Find the indicated sums for the following Geometric Progressions.
(i) 2, 6, 18, ... Find S₇.

Answer 1

In the given G.P., we have t₁ = 2, t₂ = 6 and t₃ = 18.
Thus, we have the first term, i.e., a = t₁ = 2, and the common ratio, i.e., $r=\frac{t_2}{t_1}=\frac{6}{2}=3>1$.
We know that the sum of the first n^th term of the G.P. is $S_n=\frac{a\left(r^n-1\right)}{\left(r-1\right)}$ for r > 1.
To find S₇, we will take a = 2, r = 3 and n = 7.
Thus, we have:

$$\begin{gathered} S_7=\frac{2(3^7-1)}{3-1} \\ =\frac{2(2187-1)}{2} \\ =2186 \end{gathered}$$