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The Sum S of First N Even Natural Numbers is Given by the Relation S = N(N + 1). Find N, If the Sum is 420. - Mathematics

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Question

The sum S of first n even natural numbers is given by the relation S = n(n + 1). Find n, if the sum is 420.

Solution

S = n(n + 1)
Given, S = 420
n(n + 1) = 420
n2 + n – 420 = 0
n2 + 21n – 20n – 420 = 0
n(n + 21) – 20(n + 21) = 0
(n + 21) (n – 20) = 0
n = -21, 20
Since, n cannot be negative.
Hence, n = 20.

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 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(E) | Q: 8 | Page no. 79
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The Sum S of First N Even Natural Numbers is Given by the Relation S = N(N + 1). Find N, If the Sum is 420. Concept: Quadratic Equations.
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