Question

Find S_(6) of the sum of the geometric series. a_(1)=-384,a_(6)=12,r=(1)/(-2)

Answer 1

To find S_(6) of the sum of the geometric series, use the formula Sn = a(1 - r^n) / (1 - r), where Sn is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms. Plugging in the given values, we find that S_(6) is 8064.

Step-by-step explanation:

To find the sum of a geometric series, we can use the formula: Sn = a(1 - r^n) / (1 - r), where Sn is the sum of the series, a is the first term, r is the common ratio, and n is the number of terms.

In this case, a1 = -384, a6 = 12, and r = 1 / -2. We need to find S6. Plugging these values into the formula, we get:

S6 = (-384(1 - (-2)^6)) / (1 - (-2))

Simplifying, we have:

S6 = (-384(1 - 64)) / (1 + 2)

S6 = (-384(-63)) / 3

S6 = 8064