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Question 1063556: On Day 1, you have $3 in your wallet. On the morning of day 2, you count your money and are astonished to find that there is now $5 in your wallet. On the morning of day 3, you count your money and now there is $7 in your wallet. On day 4, you are delighted to find that you now have $9 in your wallet. This continues every day and at the beginning of each day, you count your money and find that an additional $2 has magically appeared in your wallet. Assume that you do not spend any of the money in your wallet (and that your wallet is really large and can hold a lot of $1 bills). How much money is in your wallet on the morning of day 10? on the morning of day 100?
Challenge: What if "n" represents any day. Can you find the amount of money in your wallet on Day "n"?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! On Day 1, you have $3 in your wallet. On the morning of day 2, you count your money and are astonished to find that there is now $5 in your wallet. On the morning of day 3, you count your money and now there is $7 in your wallet. On day 4, you are delighted to find that you now have $9 in your wallet. This continues every day and at the beginning of each day, you count your money and find that an additional $2 has magically appeared in your wallet. Assume that you do not spend any of the money in your wallet (and that your wallet is really large and can hold a lot of $1 bills).
How much money is in your wallet on the morning of day 10? on the morning of day 100?
Day 1:: 3
Day 2:: 3+2 = 5
Day 3::
Day 4:: 3+2+2+2 = 9
Day 10:: 3 + 9*2 = 3+18 = 21
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Challenge: What if "n" represents any day. Can you find the amount of money in your wallet on Day "n"?
Day n:: 3 + (n-1)2 = 3 + 2n-2 = 2n+1
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Cheers
Stan H.
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