Answer:
Approximately 53
Step-by-step explanation:
This is a geometric progression, because each term is found by multiplying the previous one by a constant factor.
In our case, the first term is know (a1 = 3), and the growth factor is also known (q = 1.333333).
What we are tasked to do is to find the 11th (n=11) term of the series, since it asks for AFTER the 10th roll.. That's easy with the base formula:
[tex]a_{n} = a_{1} q^{n-1}[/tex]
Let's place the values we have in the equation and solve it:
[tex]a_{10} = 3 * (1.333333)^{11-1} = 3 * (17.758) = 53.3[/tex]
So, after the 10th roll, you should need 53 dice, approximately.
