What is the sum of the first 100 positive odd numbers?

Mathematics
1

what is the sum of the first 100 positive odd numbers?

2

What is the sum of the first 100 positive odd numbers?

To find the sum of the first 100 positive odd numbers, we can use the formula for the sum of an arithmetic series. Since the positive odd numbers form an arithmetic sequence with a common difference of 2, we can calculate the sum as follows:

  1. Find the first term (a₁) and the last term (aₙ):

    • The first term (a₁) is 1, which is the first positive odd number.
    • The last term (aₙ) can be found using the formula for the nth term of an arithmetic sequence:
      aₙ = a₁ + (n - 1)d,
      where d is the common difference. In this case, d = 2.
      So, aₙ = 1 + (100 - 1) * 2 = 1 + 99 * 2 = 199.

  2. Calculate the number of terms (n):

    • Since we want to find the sum of the first 100 positive odd numbers, the number of terms is 100.

  3. Use the formula for the sum of an arithmetic series:

    • The sum (S) of an arithmetic series is given by the formula:
      S = (n/2) * (a₁ + aₙ).
      Plugging in the values we found:
      S = (100/2) * (1 + 199) = 50 * 200 = 10000.

Therefore, the sum of the first 100 positive odd numbers is 10,000.