Can you solve this sequence?

[Werg22]

Here's something I thought of the other night:

0, 1, 1, 1, 1, 5, 1, 7, 2, *, ?

You don't need to know what * is :smile:.

[drpizza]

Numerators when a fraction is simplified and the denominator is 12, starting with 0.

0/12=0 (0)
1/12 (1)
2/12 = 1/6 (1)
3/12 = 1/4 (1)
4/12 = 1/3 (1)
5/12 (5)
6/12 = 1/2 (1)
7/12 (7)
8/12 = 2/3 (2)
9/12 = 3/4 (3) <---- That's the next one
10/12=5/6 (5) <--- 5 is the one you're asking for

The 100th number in your sequence:
99/12 = 33/4 (33) Hence, you're right, I didn't need to know the 10th term.

[Werg22]

Actually drpizza,

It's not necessarily 12. All you know is that 2^2*3 factors into the denominator, and 5, 7 and 2^3 don't. It could be 12*a, where a is any number not dividable by 2, 5 or 7. So you can't say what either the 10th or 100th terms are.

But congratulations nonetheless :smile: