Find the sum of the first 12 terms of the given geometric series: 3 + 6 + 12 + 24 + . . . . (1 point)
To find the sum of the first 12 terms of the given geometric series, we first need to determine the common ratio (r).
To find the common ratio, we can divide any term by the previous term. For example, if we divide the second term (6) by the first term (3), we get:
r = 6 / 3 = 2
Now that we have the common ratio, we can use the formula for the sum of the first n terms of a geometric series:
S_n = a * (1 - r^n) / (1 - r)
where:
S_n = sum of the first n terms
a = first term
r = common ratio
n = number of terms
Plugging in the values for the given series (a = 3, r = 2, n = 12), we get:
S_12 = 3 * (1 - 2^12) / (1 - 2)
S_12 = 3 * (-4095) / (-1)
S_12 = 12285
Therefore, the sum of the first 12 terms of the given geometric series is 12285.