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Question
Sum of 1 to n natural number is 45, then find the value of n.
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Solution
Natural numbers are 1, 2, 3 ......... n in AP.
Where, a = 1, d = 1
Sn = 45
∴ Sn = `n/2 [2a + (n - 1)d]`
⇒ 45 = `n/2 [2 xx 1 + (n - 1) xx 1]`
⇒ 90 = n[2 + n – 1]
∴ 90 = n[n + 1]
∴ n2 + n – 90 = 0
⇒ n2 + 10n – 9n – 90 = 0
⇒ n(n + 10) – 9(n + 10) = 0
⇒ (n + 10)(n – 9) = 0
∴ n + 10 = 0
or n – 9 = 0
∴ n = – 10
or n = 9
∴ n cannot be negative.
∴ n = 9
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