What is the sum of all odd terms between 2 and 100?

Given:

We are asked to find the sum of all odd terms between 2 and 100.

Formula used:

The odd terms between 2 and 100 are the odd numbers from 3 to 99, which form an arithmetic progression (A.P.) with:

First term, a = 3

Common difference, d = 2

Last term, l = 99

To find the sum of an A.P., we use the formula:

S_n = n/2 × (a + l)

Where, n = number of terms, a = first term, l = last term

Calculations:

First, let's find the number of terms, n, in the A.P. using the formula for the nth term of an A.P.:

l = a + (n - 1) × d

99 = 3 + (n - 1) × 2

⇒ 99 - 3 = (n - 1) × 2

⇒ 96 = (n - 1) × 2

⇒ n - 1 = 48

⇒ n = 49

Now, substitute the values into the sum formula:

S₄₉ = 49/2 × (3 + 99) = 49/2 × 102 = 49 × 51 = 2499

∴ The sum of all odd terms between 2 and 100 is 2499.