Question

the sum of all off numbers between 200 and 300 is ​

Answer 1

${\textbf{\underline{ S_{50} = 12500 }}}$

$\huge{\textbf{\underline{Correct Question:-}}}$

The sum of all odd numbers between 200 and 300 is ?

$\huge{\textbf{\underline{Solution:-}}}$

Let the first term be a and last term be L.

Odd numbers between 200 and 300 are :-

201 , 203 , 205 ...................297 , 299

a = 201

L = 299

d = 203 - 201 = 2

Let the number of odd terms be n.

$a_n = a + (n-1)d$

$299 = 201 + (n-1)2$

$299 -201 = (n-1)2$

$98 = (n-1)2$

$(n-1)= 49$

$\therefore n = 50$

$\large{\textbf{\underline{By using Summation Rule :-}}}$

$S_n = \dfrac{n}{2}( a + L)$

$S_{50} = \dfrac{50}{2}( 201 + 299)$

$S_{50} = 25 \times 500$

$\therefore S_{50}= 12500$

hence,

Required sum is 12500.