find the sum of the geometric series using a formula 1-4+16-64+256-1024
To find the sum of a geometric series using a formula, we need to know the first term (a), the common ratio (r), and the number of terms (n). In your case, the first term is 1, the common ratio is -4, and the number of terms is 6.
The formula to find the sum of a geometric series is given by:
S = (a * (1 - r^n)) / (1 - r)
Plugging in the values:
a = 1 (first term)
r = -4 (common ratio)
n = 6 (number of terms)
S = (1 * (1 - (-4)^6)) / (1 - (-4))
Let's simplify this:
S = (1 * (1 - 4096)) / (1 + 4)
Next, we calculate the numerator:
1 - 4096 = -4095
Now, we calculate the denominator:
1 + 4 = 5
So, we have:
S = (-4095) / 5
Finally, evaluating the expression:
S = -819
Therefore, the sum of the geometric series 1 - 4 + 16 - 64 + 256 - 1024 is -819.
a = 1 , r = -4
you are showing 6 terms, so
sum(6) = a(r^6 - 1)/(r-1)
= 1((-4)^6 - 1)/(-4-1)
= 4095/-5
= -819