Question

find out the sum of all odd no. from 50 to 200. plz give method also...

Answer 1

This Question can be easily solved by using the formula of Arithematic Progression (AP).

If we begin from 50 then 51 will be first odd number and if we end at 200 then 199 shall be the last term of odd number.

Now the difference between any two consecutive odd number is always 2.

Therefore, the following data are given :-

a = 51

l ( an) = 199

d = 2

TO FIND :- sum of 'n' terms

SOLUTION :-

First of all we will find the total number of terms does this AP has by this formula ;

${a}_{n} = a + (n - 1)d \\ \\ \implies 199 = 51 + (n - 1)2 \\ \\ \implies \frac{148}{2} = n - 1 \\ \\ \implies 74 = n - 1 \\ \\ \implies \boxed{n = 75}$

Now, we will find sum of the AP by using the below formula ;

${s}_{n} = \frac{n}{2} (a + l) \\ \\ = \frac{75}{2} (51 + 199) \\ \\ = \frac{75}{2} \times 250 \\ \\ = \boxed{ 9375}$

Therefore, sum of all odd numbers from 50 to 200 is 9375.