The formula to find the sum S of the first n | vedclass

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(A) Given the formula for the sum of the first $n$ natural numbers is $S = \frac{n(n+1)}{2}$.We are given $S = 300$,so we have the equation $\frac{n(n

Vedclass · Accepted Answer

$24$

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(A) Given the formula for the sum of the first $n$ natural numbers is $S = \frac{n(n+1)}{2}$.We are given $S = 300$,so we have the equation $\frac{n(n+1)}{2} = 300$.Multiplying both sides by $2$,we get $n(n+1) = 600$.Expanding this,we get $n^2 + n - 600 = 0$.To solve this quadratic equation,we look for two numbers that multiply to $-600$ and add to $1$. These numbers are $25$ and $-24$.So,$(n + 25)(n - 24) = 0$.This gives $n = -25$ or $n = 24$.Since $n$ represents the count of natural numbers,it must be positive.Therefore,$n = 24$.

The formula to find the sum $S$ of the first $n$ natural numbers is $S = \frac{n(n+1)}{2}$. Find $n$ if the sum of the first $n$ natural numbers is $300$.

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