Question

find the value of n, if the sum of the first n even natural number is 462 (ans. n=21

Answer 1

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Answer 2

Answer : n = 21 term Step-by-step Explanation : Given : Sum of the first n even natural number (Sn) = 462 To find : n = ? Even natural numbers 2,4,6,8,..n The sum of first n even natural numbers is 462 --------- ( given ) We know that Sn = n/2 × [ 2a + ( n - 1 )d ] Where , a = first term of A.P d = common difference Substituting the given value in above formula we get, 462 = n/2 × [ 2 × 2 + ( n - 1 ) × 2 ] 462 = n/2 × [ 4 + 2n - 2 ] 462 × 2 = n( 2 + 2n ) 924 = 2n + 2n² Dividing the whole equation by 2 we get, 462 = n²+ n n² + n - 462 = 0 After simplifying we get, (n - 21)(n + 22) = 0 n = 21 or n = -22 Since n cannot be negative, So n = 21