Question

A geometric sequence {an} 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)5103.3735

Step-by-step explanation

The recursive definition of the given sequence is;

`f(1) = a_1 = 6`

and

`f(n) = a_n = (1.2) * f(n - 1)`

The explicit definition is

`f(n) = a_n =6 (1.2)^(n - 1)`

We substitute n=38 to obtain:

`f(38) = a_ {38}= 6(1.2)^(37)`

`f(38) = 5103.3735`

The correct choice is C.