Question

Find the sum of the first four terms of the geometric series 60 + 30 + 15 + …

Answer 1

Given series,

$60+30+15+.....$

Solution:

Here,

$\begin{gathered} a_1=60 \\ r=\frac{1}{2} \\ n=4 \end{gathered}$

We substitute these values into the formula for the sum of the first n terms of a geometric sequence and simplify.

$\begin{gathered} S_n=\frac{a_1-a_1r^n}{1-r} \\ S_4=\frac{60-60\left(\frac{1}{2}\right?^4}{1-\frac{1}{2}} \\ S_4=\frac{60-60\times\frac{1}{16}}{\frac{1}{2}} \\ S_4=\frac{60-\frac{60}{16}}{\frac{1}{2}} \end{gathered}$

Further solved as,

$\begin{gathered} S_4=\frac{\frac{960-60}{16}}{\frac{1}{2}} \\ S_4=\frac{\frac{900}{16}}{\frac{1}{2}} \\ S_4=\frac{1800}{16} \\ S_4=112.5 \end{gathered}$

Thus, the sum of the first four terms is 112.5