Question

Question:-

How many consecutive natural numbers starting from one should be added to get 300?

Answer 1

Answer:

The number series 1, 2, 3, 4, . . . . , 299, 300. Therefore, 45150 is the sum of positive integers upto 300.

Answer 2

$\bf\red{QuestioN:-}$

How many consecutive natural numbers starting from one should be added to get 300?

$\bf\green{AnsweR:-}$

The concept we used here is,

$\large{\boxed{\bf{\longrightarrow\dfrac{n(n+1)}{2}}}}}$

Then, according to the given question,

$\longrightarrow\bf{\dfrac{n(n+1)}{2}=300}$

$\longrightarrow\bf{n^2+1=300\times2=600}$

$\longrightarrow\bf{n^2+1-600=0}$ ------------- Eq formed

Now we got an equation here.  

So, now we can use another concept here. That is,

$\large{\boxed{\bf{n=\dfrac{-b+/-\sqrt{b^2-4ac}}{2a}}}}}}$

Here,

• a = 1

• b = 1

• c = 600

$\longmapsto\bf{n=\dfrac{-b+/-\sqrt{b^2-4ac}}{2a}}$

$\longmapsto\bf{n=\dfrac{-1+/-\sqrt{1^2-4\times1\times-600}}{2\times1}}$

$\longmapsto\bf{n=\dfrac{-1+/-\sqrt{1+2400}}{2}}$

$\longmapsto\bf{n=\dfrac{-1+/-\sqrt{2401}}{2}}$

$\longmapsto\bf{n=\dfrac{-1+/-(49)}{2}}$

$\longmapsto\bf{n=\dfrac{-1+49}{2}~/~\dfrac{-1-49}{2}}$

$\longmapsto\bf{n=\dfrac{48}{2}~/~\dfrac{-50}{2}}$

$\longmapsto\bf{n=24~/~-25}$

Number of natural numbers can't be negative.  

So the answer is 24.

Happy Learning!!