Question

Sum of the first n' natural
numbers is 231. what number
is 'n?​

Answer 1

Given:

• Sum of n natural numbers is 231.

To Find:

• The value of n .

Answer:

Given that the sum of first n nautural numbers is 231.

⇒ n(n+1)/2 = 231.

⇒n(n+1) = 231 ×2 .

⇒ n² + n = 462 .

⇒ n² + n - 462 = 0 .

⇒n² + 22n - 21n - 462 = 0.

⇒n( n + 22 ) - 21( n +22 ) = 0.

⇒ ( n + 22 ) ( n - 21 ) = 0 .

⇒ n = 21 , -22 .

Since n can't be negative ;

Hence n = 21 .

Hence the value of n is 21.

Step-by-step explanation:

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