Question

A boy is excited about his approaching birthday. He collects 1 leaf on the first day of the month, 2 leaves on the second day and 3 leaves on the third day of the month and so on. On his birthday, he finds that he has collected 210 leaves in all. On which day of the month is his birthday?

Answer 1

Here sum = 210
first term is 1
common difference = 1
Sum of AP = n/2(2a+(n-1)d)
n/2(2+n-1)= 210
n²+n = 420
n²+n-420=0
n²+21n-20n-420=0
n(n+21) -20(n+21)=0
(n+21) ( n-20) =0
either n = -21 or n =20
since n= -21 not possible so
answer is n= 20
boy will have his b'day on 20