Question

Find the sum of all odd numbers between 100 and 200.

Answer 1

Hint: Here we will use the arithmetic progression concepts to find the sum of all odd numbers between 100 and 200.

Complete step-by-step answer:

You have to find out the sum of all odd numbers between 100 and 200.
In terms of series it is written as $101 + 103 + 105 + ............. + 199$.
So you know this form an A.P with first term$({a_1}) = 101$and last term$({a_l}) = 199$with common difference$(d) = 103 - 101 = 2$.
First find out the number of terms,
\[
   \Rightarrow ({a_l}) = ({a_1}) + (n - 1)d \\
   \Rightarrow 199 = 101 + (n - 1)2 \\
   \Rightarrow \dfrac{{199 - 101}}{2} + 1 = n \\
   \Rightarrow n = 50 \\
\]
Sum of the given series is ${S_n} = \dfrac{n}{2}({a_1} + {a_l})$
$ \Rightarrow {S_n} = \dfrac{{50}}{2}(199 + 101) = 25(200) = 5000$
So this your required sum.

Note: In this type of question always remember the formulas of Arithmetic Progression (A.P), it will help you find your desired answer.