the sum of first n even natural no is given by the relation s=n×n-1 . find n and n-1 . find n if the sum is 240
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S = n(n-1)
⇒240 = n²- n
⇒n² - n - 240 = 0
⇒n² - 16n + 15n -240 =0
⇒n(n-16) + 15(n-16) = 0
⇒(n-16)(n+15) = 0
So n = 16 or n = -15
But number of even natural numbers cant be negative
so n= 16
and n-1= 15
⇒240 = n²- n
⇒n² - n - 240 = 0
⇒n² - 16n + 15n -240 =0
⇒n(n-16) + 15(n-16) = 0
⇒(n-16)(n+15) = 0
So n = 16 or n = -15
But number of even natural numbers cant be negative
so n= 16
and n-1= 15
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