Question

The first five terms of a sequence are shown.5, 15, 45, 135, 405Which function models the value of the nth term?O A. f (x) = 5(3)"_?O B. f(x) = 3(5)"O c. f(x) = 3(5)"}OD. f(x) = 10(5)*-!

Answer 1

The first five terms of the sequence are: 5, 15, 45, 135, 405

The nth term of the sequence is given by:

$\text{ T}_n=ar^{n-1}$

a = first term of the sequence =5

r = common ration = 3

Note that the common ratio is calculated by diving each term by its previous term. For instance, 15 divided by 5 is 3.

Therefore,

$\text{ T}_n=5(3)^{n-1}$

The function which models the n-th term of the sequence is

$f(x)=5(3)^{x-1}$

Option A is the right one