The sum of a geometric sequence can be calculated using the formula:
S = a * (1 – r^n) / (1 – r)
where:
- S is the sum of the sequence.
- a is the first term of the sequence.
- r is the common ratio.
- n is the number of terms.
In this case, the terms of the sequence are:
- First term (a) = 1
- Second term = 3
- Third term = 9
From these terms, we can see that the common ratio (r) can be calculated as follows:
- r = Second term / First term = 3 / 1 = 3
- r = Third term / Second term = 9 / 3 = 3
Now, we know:
- a = 1
- r = 3
- n = 12
Substituting these values into the formula gives:
S = 1 * (1 – 3^12) / (1 – 3)
Now we calculate:
- 3^12 = 531441
- 1 – 531441 = -531440
- S = 1 * (-531440) / -2
- S = 531440 / 2 = 265720
So, the sum of the geometric sequence with 12 terms is 265720.