Final answer:
To find the sum of the first 8 terms of the geometric sequence, the common ratio is identified as -1/2, and the sum formula for geometric series is applied.
Step-by-step explanation:
The student is asked to find the sum of the first 8 terms of a geometric sequence. To solve this, we first need to identify the common ratio of the sequence. The given sequence is 16, -8, 4, ... The common ratio (r) can be found by dividing the second term by the first term (r = −8 ÷ 16 = -½). Now that we have the common ratio, we can use the formula for the sum of the first n terms of a geometric series: Sn = a(1 - rn) ÷ (1 - r), where 'a' is the first term of the sequence, 'r' is the common ratio, and 'n' is the number of terms to sum. Substituting the known values into the formula gives us the sum of the first 8 terms: S8 = 16(1 - (-½)8) ÷ (1 - (-½)) = 16(1 - ½)8 ÷ 1.5. By calculating this, we can find the sum rounded to the nearest hundredth if necessary.