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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

$24$

Vedclass · Answer

(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 $300$.

Similar Questions

The product of the digits of a two-digit number is $15$. If the digits of this number are interchanged,the new number so obtained is $18$ more than the original number. Find the original number.

The roots of a quadratic equation $6 x^{2}-13 x+6=0$ are .... .

Check whether the equation $6x^2 - 7x + 2 = 0$ has real roots, and if it has, find them by the method of completing the squares.

Obtain the roots of the following equation using the method of 'completing the square': $m^{2} - 18m + 81 = 0$

Vedclass Test Series

Exam Paper Generator

Online Exam Module