Sum of Odd Numbers between 100 and 200

To find the sum of all odd numbers lying between 100 and 200, we need to identify the odd numbers in this range and then calculate their sum.

Identifying Odd Numbers

Odd numbers are integers that are not divisible by 2. In other words, when an odd number is divided by 2, it leaves a remainder of 1.

Identifying Odd Numbers between 100 and 200

To identify the odd numbers between 100 and 200, we can start with the first odd number in this range, which is 101, and then add 2 to it repeatedly until we reach the last odd number in the range.

Starting with 101, the subsequent odd numbers can be obtained by adding 2:
101, 103, 105, 107, 109, 111, 113, ..., 197, 199

Calculating the Sum

To calculate the sum of these odd numbers, we can use the formula for the sum of an arithmetic series:

Sum = (n/2)(first term + last term)

In this case, the first term is 101, the last term is 199, and n is the number of terms in the series.

To find the number of terms in the series, we can use the formula:

n = (last term - first term)/2 + 1

Substituting the values, we get:

n = (199 - 101)/2 + 1
n = 99/2 + 1
n = 49.5 + 1
n = 50.5

Since we cannot have a fraction of a term, we round down to the nearest whole number. Therefore, n = 50.

Now, we can calculate the sum:

Sum = (50/2)(101 + 199)
Sum = 25(300)
Sum = 7500

Conclusion

The sum of all odd numbers lying between 100 and 200 is 7500. Therefore, the correct answer is option A) 7500.