Question

Find the sum of all positive odd integers less than 100 by arithmetic progression

Answer 1

To find the sum of an arithmetic progression, we need to know the first term, the last term, and the common difference.

In this case, the first term is 1 (the smallest odd number), the common difference is 2 (since we are adding 2 to each term to get the next odd number), and the last term is 99 (the largest odd number less than 100).

We can find the number of terms (n) in this arithmetic progression using the formula:

n = (last term - first term) / common difference + 1
= (99 - 1) / 2 + 1
= 49

Now, we can find the sum of this arithmetic progression using the formula:

Sum = (n / 2)(first term + last term)
= (49 / 2)(1 + 99)
= 24.5 * 100
= 2450

Therefore, the sum of all positive odd integers less than 100 is 2450.