Question

What is the sum of the first 8 terms of the geometric series:

3+6+12+24+...

Answer 1

Answer:

The sum of the first 8 terms of the given geometric series is 765.

Step-by-step explanation:

The given series in the geometric progression is $3,6,12,24,...$

Its initial term is $a=3$ and its common ratio is $r=\frac{6}{3}=2$

We are required to find the sum of the first 8 terms of the series.

The sum of n terms of the geometric series is given by the relation

$S_{n}=\frac{a(r^n-1)}{r-1}$

Substituting the known values in the above relation we get

$S_{8}=\frac{3(2^8-1)}{2-1} =3(256-1)=765$

Therefore,

The sum of the first 8 terms of the given geometric series is 765.

#SPJ3