Question

Find the sum of all odd numbers between (i) 0 and 50 (ii) 100 and 200.

Answer 1

(i) In this problem, we need to find the sum of all odd numbers lying between 0 and 50.

So, we know that the first odd number after 0 is 1 and the last odd number before 50 is 49.

Also, all these terms will form an A.P. with the common difference of 2.

So here,

First term (a) = 1

Last term (l) = 49

Common difference (d) = 2

So, here the first step is to find the total number of terms. Let us take the number of terms as n.

Now, as we know,

So, for the last term,

Further simplifying,

Now, using the formula for the sum of n terms,

For n = 25, we get,

On further simplification, we get,

Therefore, the sum of all the odd numbers lying between 0 and 50 is.

(ii) In this problem, we need to find the sum of all odd numbers lying between 100 and 200.

So, we know that the first odd number after 0 is 101 and the last odd number before 200 is 199.

Also, all these terms will form an A.P. with the common difference of 2.

So here,

First term (a) = 101

Last term (l) = 199

Common difference (d) = 2

So, here the first step is to find the total number of terms. Let us take the number of terms as n.

Now, as we know,

So, for the last term,

Further simplifying,

Now, using the formula for the sum of n terms,

For n = 50, we get,

Therefore, the sum of all the odd numbers lying between 100 and 200 is.