A geometric sequence is defined by the function f (1) = a1 = 6 and f (n) = an = (1.2) * f (n - 1) for n ≥ 2. Find f (38). A) 273.6 B) 326.26 C) 5103.3735 D) 6124.0482

Given that the geometric series is given by:

f (n) = an=1.2f (n-1) where a1=6, then f (38) will be found as follows:

a2=1.2f (2-1) = 1.2f (1) = 1.2*6=7.2

a3=1.2f (3-1) = 1.2f (2) = 8.64

thus the common ratio is r=1.2

but

explicit formula for geometric sequence is:

an=ar^ (n-1)

thus plugging our values:

f (38) = 6 (1.2) ^ (38-1)

f (38) = 5103.3735

Answer: C) 5103.3735