Question

For the geometric series 2 + 6 + 18 + 54 + ... , find S8

Answer 1

Answer:

$\displaystyle S_{8}=6560$

Step-by-step explanation:

We have the geometric sequence:

2, 6, 18, 54 ...

And we want to find S8, or the sum of the first eight terms.

The sum of a geometric series is given by:

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

Where n is the number of terms, a is the first term, and r is the common ratio.

From our sequence, we can see that the first term a is 2.

The common ratio is 3 as each subsequent term is thrice the previous term.

And the number of terms n is 8.

Substitute:

$\displaystyle S_8=\frac{2((3)^{8}-1)}{(3)-1}$

And evaluate. Hence:

$\displaystyle S_8=6560$

The sum of the first eight terms is 6560.

Answer 2

Answer:

S₈ = 6560

Step-by-step explanation:

The sum to n terms of a geometric sequence is

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

where a is the first term and r the common ratio

Here a = 2 and r = $\frac{a_{2} }{a_{1} }$ = $\frac{6}{2}$ = 3 , then

S₈ = $\frac{2(3^{8}-1) }{3-1}$

    = $\frac{2(6561-1)}{2}$

    = 6561 - 1

    = 6560