geometric sequence

[misstina]

Use the geometric sequence of numbers 1, 1/2, 1/4, 1/8,…to find the following:
a) What is r, the ratio between 2 consecutive terms?
Answer: -1/2
Show work in this space.

1/8 divided by 1/4

Is the above correct? And if so, how do I do the next:

b) Using the formula for the sum of the first n terms of a geometric series, what is the sum of the first 10 terms? Please round your answer to 4 decimals.

 

[galactus]

For part 1, r=1/2.


The nth partial sum of a geometric series is given by :

\(\displaystyle S_{n}=a_{1}\left(\frac{1-r^{n}}{1-r}\right)\)

a_1=first term in series, r=ratio(above), n=partial sum, in your case, 10