Question

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

Answer 1

C

Explanation:

The formula is an = a1*r(n - 1) . So, a38 = 6(1.2)37.

Answer 2

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