Question

A contestant on a game show wins $100 for answering

a question correctly in Round 1. In each subsequent
round, the contestant's winnings are doubled if she
gives a correct answer. If the contestant gives an
incorrect answer, she loses everything. Use this
information for Items 21-23.
21. Write an explicit formula that gives
the
contestant's winnings in round n, assuming she
answers all questions correctly.
22. How much does the contestant win in Round 10,
assuming she answers all questions correctly?
23. How many rounds does a contestant need to play
in order to answer a question worth at least
$1,000,000?

Answer 1

21. An= 100 (2)^n-1

22. $51,200

23. n= 15

Explanation:

21. 100, 200, 400, 800, 1600...

An= A r ^n-1

22. a10= 100(2)^10-1

a10= 100(2)^9

23. n=14

a14= 100(2)^14-1= 819200

n= 15

a15= 100(2)^15-1= 1638400