Your password must be created only using the numbers 0 to 9 with repeated numbers allowed. If your password is four numbers long, how many ways can you create a password? Do not include commas in your answer, for example, 1,000 would be written as 1000.

10000

Step-by-step explanation:

yeah-ya right?

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for