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

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:

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:

And evaluate. Hence:

The sum of the first eight terms is 6560.

S₈ = 6560

Step-by-step explanation:

The sum to n terms of a geometric sequence is

=

where a is the first term and r the common ratio

Here a = 2 and r = = = 3 , then

S₈ =

    =

    = 6561 - 1

    = 6560

answer: y=4000x+14000

step-by-step explanation: