I'm thinking of doing some sort of lottery like thing, only instead of buying tickets, people buy guesses at dice rolls. The first in line gets to guess first, and if they guess right, the lottery's over, and they win.

Getting a guess earlier is better, of course, so it's more expensive. I figure each subsequent guess costs a sixth of the previous, if the guess is placed on one dice.

This gives:

$\displaystyle \displaystyle \text{cost of wager} = \frac{\text{initial guess cost}}{6^{\text{number of guesses } -1}}$ (1)

I wanna draw myself a pretty little graph where the number of guesses are x, and the total of all wagers so far is y, but have managed to forget almost literally everything I was ever taught about sequences. I tried to rearrange $\displaystyle \frac{1}{6}a(n-1) = a_{n}$ to find r, but just ended up with (1).

Could anyone point me in the right direction please?