Question

Need Some Help With Explicit Functions

Answer 1

Answer:

$f(1)=14000$

$f(n)=f(n-1) \cdot 0.9$

$10206$ is the next term after the third one given.

Step-by-step explanation:

This geometric since term divided by previous is the same number each time (the result that you get here is called the common ratio).

That is we have:

12600/14000=0.9

and

11340/12600=0.9

This means:

$\frac{\text{ term}}{\text{ previous term}}=0.9$

More formally:

$\frac{a_n}{a_{n-1}}=0.9$

To get it in the mentioned form you need to solve for $a_n$.  So we need to multiply both sides by $a_{n-1}$ giving you:

$a_n=0.9 a_{n-1}$

They used f( ) notation instead so this:

$f(n)=0.9f(n-1)$.

In general when doing recursive you have to least give one term for the sequence (in some cases more than one).

f(1) means what is the first term.  The first term is 14000, so $f(1)=14000$.

The next term can be found by multiply your common ratio to the term before.

$11340 \cdot 0.9=10206$ is the next term.