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If 1 2 - a 1 + 2 2 - a 2 + 3 2 - a 3 + . … … . . + n 2 - a n = 1 3 n n 2 - 1 , then the value of a 7 is

Correct answer

7

Step-by-step solution

1 2 + 2 2 + 3 3 + . … … + n 2 - a 1 + a 2 + a 3 + . … … + a n = 1 3 n n 2 - 1 Replace n by n - 1 1 2 + 2 2 + 3 3 + . … … + n - 1 2 - a 1 + a 2 + a 3 + . … … + a n - 1 = 1 3 n - 1 n - 1 2 - 1 Subtracting these two equations, we get, n 2 - a n = 1 3 n - 1 n n + 1 - n 2 + 1 - 2 n - 1 = 1 3 n - 1 n 2 + n - n 2 + 2 n = n 2 - n ⇒ a n = n ⇒ a 7 = 7

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