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The Sum S of N Successive Odd Numbers Starting from 3 is Given by the Relation N(N + 2). Determine N, If the Sum is 168. - Mathematics

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Question

The sum S of n successive odd numbers starting from 3 is given by the relation n(n + 2). Determine n, if the sum is 168.

Solution

From the given information, we have:
n(n + 2) = 168
n² + 2n – 168 = 0
n² + 14n – 12n – 168 = 0
n(n + 14) – 12(n + 14) = 0
(n + 14) (n – 12) = 0
n = -14, 12
But, n cannot be negative.
Therefore, n = 12.

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APPEARS IN

 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(D) | Q: 1 | Page no. 78
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The Sum S of N Successive Odd Numbers Starting from 3 is Given by the Relation N(N + 2). Determine N, If the Sum is 168. Concept: Quadratic Equations.
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