SOLUTION: Professor McGonagall gave Hermione one nickel on Monday. On Tuesday, she gave Hermione five nickels. On Wednesday, she gave Hermione 14 nickels and on Thursday, she gave Hermione 3

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: Professor McGonagall gave Hermione one nickel on Monday. On Tuesday, she gave Hermione five nickels. On Wednesday, she gave Hermione 14 nickels and on Thursday, she gave Hermione 3      Log On

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Question 504967: Professor McGonagall gave Hermione one nickel on Monday. On Tuesday, she gave Hermione five nickels. On Wednesday, she gave Hermione 14 nickels and on Thursday, she gave Hermione 30 nickels. Professor McGonagall told Hermione that if she could figure out the pattern and tell her how many nickels she would get on the tenth day, Hermione could have them all on Friday.


How many nickels should Hermione tell Professor McGonagall she will get on the tenth day?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I call the day number d, then
when +d+=+1, number of nickels is +0+%2B+d%5E2+ = 1
when +d+=+2+, number of nickels is +1+%2B+d%5E2+ = 5
when +d+=+3+, number of nickels is +5+%2B+d%5E2+ = 14
when +d+=+4+, number of nickels is +14+%2B+d%5E2+ = 30
So, on any given day, d, she gets the number that she got
the number she got the previous day plus +d%5E2+ more.
On the 10th day, she got
10%5E2 + number on the previous day
On the 9th day, she got
9%5E2 + number on previous day
On the 8th day, she got
8%5E2 + number on previous day
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Notice this is

+100+%2B+81+%2B+64+%2B+49+%2B+36+%2B+25+%2B+16+%2B+9+%2B+4+%2B+1+=+385