The first four terms of a sequence are shown.

16, 48, 144, 432, ...

What is the explicit function, f (n), that defines the sequence? Explain how you determined your

answer. Write your answer in the space provided.

The explicit function is f (n) = 3f (n - 1)

Solution:

Given, sequence is 16, 48, 144, 432 ...

We have to find the explicit function.

Now, if we observe the given sequence, every term is three times its previous term.

That is, the next term in sequence is obtained by multiplying the previous term by 3

48 = 16 x 3

144 = 48 x 3

432 = 144 x 3

So, explicit function f (n) will be

nth term = 3 x (n - 1) th term

F (n) = 3 x f (n - 1) [ since nth term is f (n) ]

We derived the above function just by generalizing the sequence and making it into the function.

The nth term is obtained by multiplying the n - 1 term with 3

Hence explicit function is f (n) = 3f (n - 1)