For the geometric sequence, find the sum of the specified number of terms. The first 8 terms of 4, -12, 36, ...
S8=

Given:

The geometric sequence is

To find:

The sum of first 8 terms of the given geometric sequence.

Solution:

We have,

Here, the first term is 4 and the common ratio is

The sum of first n terms of a geometric sequence is

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

Putting n=8, a=4 and r=-3, we get

Therefore, the sum of first 8 terms is -6560.

the right system of equations to describe the situation would

be on the form:

x1 = 8000 + y1*t

and

x2 = 8000 + y2*t

where x1 and x2 represents the total money of imogene and her

friend respectively at the end of t years.

now for the value of amount earned, y1 and y2:

y1=8000*0.08

y2=2000*√(t-2)