Answer:16
Step-by-step explanation:To find the sum of an infinite geometric sequence, you can use the formula for the sum of an infinite geometric series:
S = a / (1 - r)
Where:
S is the sum of the infinite series.
a is the first term of the sequence.
r is the common ratio between consecutive terms.
In your case, the first term (a) is 12, and the common ratio (r) can be found by dividing the second term by the first term and the third term by the second term:
r = (3/4) / 3 = (3/4) / (12) = 1/4
Now, plug these values into the formula:
S = 12 / (1 - 1/4)
Simplify the denominator:
S = 12 / (3/4)
To divide by a fraction, multiply by its reciprocal:
S = 12 * (4/3)
Now, multiply:
S = (12 * 4) / 3
S = 48 / 3
S = 16
So, the sum of the infinite geometric sequence 12, 3, 3/4 is 16.