Calculate S12 for the geometric series 4+10+25+...
A. 158,943.053
B. 95,367.432
C. 63,575.621
D -345.990
To calculate the sum of the first 12 terms of a geometric series, we use the formula:
Sn = a(1 - r^n) / (1 - r)
Where Sn is the sum of the first n terms, a is the first term, r is the common ratio, and n is the number of terms.
In this case, a = 4, and r is the ratio between any two consecutive terms. To find r, we divide any term by its previous term:
r = 10/4 = 5/2 = 2.5
Now we can substitute these values into the formula:
S12 = 4(1 - (2.5)^12) / (1 - 2.5)
S12 = 4(1 - 244.14) / (-1.5)
S12 = 4(-243.14) / (-1.5)
S12 = 972.56 / 1.5
S12 = 648.37...
Therefore, the correct answer is not provided.