To find the sum of the geometric sequence where the first three terms are 1, 3, and 9, we first need to identify the first term and the common ratio. Here, the first term (a) is 1 and the common ratio (r) can be calculated by dividing the second term by the first term:
r = 3 / 1 = 3
The general formula for the sum (Sn) of the first n terms of a geometric sequence is given by:
Sn = a * (1 - rn) / (1 - r)
In our case, a = 1, r = 3, and n = 14. Plugging these values into the formula gives:
S14 = 1 * (1 - 314) / (1 - 3)
Now, we calculate:
314 = 4782969
So:
S14 = (1 - 4782969) / (1 - 3)
S14 = (-4782968) / (-2)
S14 = 2391484
Thus, the sum of the first 14 terms of the geometric sequence 1, 3, 9 is 2,391,484.