Question

If the sum of first natural numbers is 91 .find n

Answer 1

Answer:

Sum of first n natural number = 91

a=1, d=1 (we know the the given sum is of first n natural number)

$sn = \frac{n}{2}(2a + (n - 1)d \\ 91 = \frac{n}{2}(2 \times 1 + (n - 1) \times 1 \\ 91 \times 2 = n(2 + n - 1) \\ 182 = n(1 + n) \\ 182 = {n}^{2} + n \\ 0 = {n}^{2} + n - 182 \\ 0 = {n}^{2} + 14 n - 13n + 182 \\ 0 = n(n + 14) + - 13(n + 14) \\ 0 = (n + 14)(n - 13) \\ n = - 14..13 \\ it \: is \: not \: negative \: so \: we \: take \: 13 \: \\ ans is \: 13$

Step-by-step explanation:

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