Answer:
The general form of geometric series is ⇒ [tex]x_{n} = a * r^{n-1}[/tex]
Where a is the first term and r is the common ratio
The sum of n terms of the geometric series is ⇒ [tex]S_{n} = a * (\frac{1-r^n}{1-r} )[/tex]
For the given geometric series 2, 8, 32, 128
The first term is a = 2
The common ratio r = 8/2 = 32/8 = 128/32 = 4
So, [tex]x_{n} = 2 * 4^{n-1}[/tex]
And the sum of the given terms:
n = 4
∴ [tex]S_{n} = 2 * (\frac{1-4^4}{1-4} ) = 2 * (\frac{1-256}{1-4} ) = 2 * (\frac{255}{3} ) = 170[/tex]
