Final answer:
The sum of the first 7 terms of the geometric sequence -1, 3, -9, 27, ... is -547. This is calculated using the geometric series sum formula with a common ratio of -3.
Step-by-step explanation:
The student has asked for the sum of the first 7 terms of the geometric sequence -1, 3, -9, 27, .... This sequence has a common ratio of -3 (each term is multiplied by -3 to get the next term). To find the sum of the first n terms of a geometric sequence, we use the formula:
Sn = a1(1 - rn) / (1 - r),
where a1 is the first term, r is the common ratio, and n is the number of terms.
Using the formula, we calculate:
S7 = (-1)(1 - (-3)7) / (1 - (-3)) = (-1)(1 + 2187) / 4 = (-1)(2188) / 4 = -547.
The sum of the first 7 terms of the given geometric sequence is -547, which corresponds to Option 2.