Answer to Question #90551 in Algebra for Shifa naaz

Question

is approaching.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

Let n birthday in digital form, then we have an arithmetic sequence with a difference of 1, where the first term is 1, and the last term is n.

Denote the sum of the first n terms by S_n

the sum of the first n terms of an arithmetic sequence is

Sn = [(a₁ + a_n)/2]*n

According to the question statement,

210 =[(1+n)/2]*n

210 =(n+n²)/2

420 = n+n²

n+n²-420 = 0

n² +21n -20n -420 = 0

(n-20)*(n+21) = 0

n₁ =20 n₂ = -21

since the date of the month is a positive date, n = 20.

The 20th day of the month is a birthday.

Answer: 20.