Q12 of 83 Page 90

The formula of the sum of first n natural numbers is S = . If the sum of first n natural number is 325, find n.


And, S = 325



⇒ n2 + n = 325(2)


⇒ n2 + n – 650 = 0


⇒ n2 + (26 – 25)n – 650 = 0


⇒ n2 + 26n – 25n – 650 = 0


⇒ n(n + 26) – 25(n + 26) = 0


⇒ (n – 25)(n + 26) = 0


⇒ n – 25 = 0 or n + 26 = 0


⇒ n = 25 or n = – 26


Given that n is a natural no.


⇒ n cannot be negative.


⇒ n = 25


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