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

$A$ train travels at a certain average speed for a distance of $63 \, km$ and then travels a distance of $72 \, km$ at an average speed of $6 \, km/h$ more than its original speed. If it takes $3 \, hours$ to complete the total journey,what is its original average speed in $km/h$?

If the following quadratic equation has two equal and real roots,then find the value of $k$: $k x^{2} - 24 x + 16 = 0$.

If the following quadratic equation has two equal and real roots,then find the value of $k$: $x(4 - kx) = 3 - 2x$.

The sum of a natural number and its reciprocal is $\frac{5}{2}$. Then the number is $\ldots \ldots .$

Find two consecutive even positive integers,the sum of whose squares is $244$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module