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=(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=(a_1-a_1r^n)/(1-r) \\ S_4=(60-60\left((1)/(2)\right?^4)/(1-(1)/(2)) \\ S_4=(60-60*(1)/(16))/((1)/(2)) \\ S_4=(60-(60)/(16))/((1)/(2)) \end{gathered}`

Further solved as,

`\begin{gathered} S_4=((960-60)/(16))/((1)/(2)) \\ S_4=((900)/(16))/((1)/(2)) \\ S_4=(1800)/(16) \\ S_4=112.5 \end{gathered}`

Thus, the sum of the first four terms is 112.5