Question

Evaluate each sequence’s related geometric series . 2,8,32,128

Answer 1

Answer:

The general form of geometric series is ⇒  $x_{n} = a * r^{n-1}$

Where a is the first term and r is the common ratio

The sum of n terms of the geometric series is ⇒ $S_{n} = a * (\frac{1-r^n}{1-r} )$

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, $x_{n} = 2 * 4^{n-1}$

And the sum of the given terms:

n = 4

∴ $S_{n} = 2 * (\frac{1-4^4}{1-4} ) = 2 * (\frac{1-256}{1-4} ) = 2 * (\frac{255}{3} ) = 170$