Find the sum of the geometric series 128-64+32-______to 8 terms .
To find the sum of a geometric series, you can use the formula:
Sn = a * (r^n - 1) / (r - 1),
where:
- Sn is the sum of the series
- a is the first term of the series
- n is the number of terms in the series
- r is the common ratio between consecutive terms
In this case, we are given the first term (a = 128), the number of terms (n = 8), and we need to find the common ratio (r).
To find the common ratio, we can use the formula:
r = (2nd term) / (1st term).
In this case, the 2nd term is -64 and the 1st term is 128. Substituting these values, we get:
r = (-64) / (128) = -1/2.
Now that we have the first term (a), the common ratio (r), and the number of terms (n), we can substitute these values into the formula for Sn to find the sum of the series:
Sn = 128 * ((-1/2)^8 - 1) / (-1/2 - 1),
Simplifying this expression will give us the sum of the geometric series.