problem 179 penguin problem

User Generated

fghqrag1621

Mathematics

Description

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?

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Explanation & Answer

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


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