A series of people donate some amount to an orphanage. The first person donates Rs. 1, the second one Rs. 4, the third one Rs. 9, the fourth one Rs. 16 and so on. After donation, by which person the total donated amount surpasses Rs. 2000.?

11^th person
18^th person
17^th person
15^th person

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

AhmedNazir

Option 2 : 18th person

⇒ The donation made by everyone is in the form of squares of integers.

Assume that donation made by nth person surpasses the tally of 2000 Rs.

⇒ 1² + 2² + 3² + 4² + ......... + n² > 2000

⇒ n/6 × (n + 1)(2n + 1) > 2000

By Hit and Trial,

⇒ Try for n = 17

n/6 × (n + 1)(2n + 1) = 17/6 × (18) (35) = 1785 < 2000

⇒ Now, try n = 18

n/6 × (n + 1)(2n + 1) = 18/6 × (19)(37) = 2109 > 2000

Hence, donation made by 18^th person will surpass the tally of Rs. 2000.

4 views Answered 2022-09-04 04:29

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