What is the sum of the first 9 terms of the geometric sequence an=7(−2)n−1 ?
To find the sum of the first 9 terms of a geometric sequence, we can use the formula:
S = a * (1 - r^n) / (1 - r)
where:
S = sum of the first 9 terms
a = first term
r = common ratio
n = number of terms
In this case, the first term (a) is 7 and the common ratio (r) is -2. The sum of the first 9 terms is:
S = 7 * (1 - (-2)^9) / (1 - (-2))
S = 7 * (1 - 512) / (1 + 2)
S = 7 * (-511) / 3
S = -3577
Therefore, the sum of the first 9 terms of the geometric sequence is -3577.