# How do you calculate the sum of odd numbers between 1 and 2001?

Refer to explanation

#### Explanation:

How many odd numbers are between 1 and 2001?

They form a sequence which general formula is

${a}_{n} = a + \left(n - 1\right) \cdot d \implies 1999 = 3 + \left(n - 1\right) \cdot 2 \implies n = 999$

Their sum is

$S = \frac{n}{2} \cdot \left({a}_{1} + {a}_{n}\right) = \frac{999}{2} \cdot \left(3 + 1999\right) \implies S = 999999$