Find the sum of the first 500 odd numbers

Josiah Owens

Josiah Owens

Answered question

2022-10-20

Find the sum of the first 500 odd numbers

Answer & Explanation

amilazamiyn

amilazamiyn

Beginner2022-10-21Added 14 answers

The first one is 1, the last is 2 × 500 - 1 = 999 . Their average is 500. Since the numbers are in an AP, the average of all 500n of them is also the same, namely 500. Thus, the sum is
500 × 500 = 250000
In general, the sum of the first n odd numbers is
n × 1 2 ( 1 + ( 2 n - 1 ) ) = n 2

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