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**Quick** There is a game that goes like this, you pay a $5 fee to begin with. A coin is then flipped until it flips tails (or the house maximum of $\displaystyle x$ flips). Each time it lands on heads the house wll give you an amount equal to $1 times the number of consecutive flips, for example, land three heads in a row gets you three dollars($3), which is then added to the money you got from landing two flips in a row($2), and the one beginning flip on heads ($1), in other words, 3 heads in a row will give you $6.

a)What would be the expected house winnings if 16 people played?

b)32 people?

c)64?

My answers:

a)54

b)103

c)200

Is there one equation to model all the answers?