problem 179 penguin problem

label Mathematics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

There are 190 penguins standing near the beach, and then one penguin dives into the sea, followed by two penguins, then three penguins, and so on, with one more penguin in each group. How many penguins will be in the last group?

Aug 21st, 2014

19 penguins in the last group

(1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19) =19

sum to n terms  is (1+2+...+n) = n(n+1)/2 =190

n(n+1) =2*190

n(n+1)-380=0

n^2+n-380=0

n^2+20n-19n-380=0

n(n+20)-19(n+20)=0

(n+20)(n-19)=0

n=19

Last group contains 19 penguins

Aug 21st, 2014

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