Final answer:
The sum of the geometric sequence -1, 6, -36... with 6 terms is approximately 952.14.
Step-by-step explanation:
A geometric sequence is a sequence of numbers where each term is found by multiplying the previous term by a constant ratio. In this case, the ratio between consecutive terms is -6, since -1 * -6 = 6, and 6 * -6 = -36. Given that there are 6 terms in the sequence, we can find the sum using the formula:
S = a * (1 - r^n) / (1 - r)
where S is the sum of the sequence, a is the first term, r is the common ratio, and n is the number of terms.
Plugging in the values:
S = -1 * (1 - (-6)^6) / (1 - (-6))
S = -1 * (1 - 46656) / (1 + 6)
S = -1 * (-46655) / 7
S = 6665 / 7
S = 952.14
Therefore, the sum of the geometric sequence -1, 6, -36... with 6 terms is approximately 952.14.