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Sum of an arithmetic series:
Sum = (1st number + last number) x (the number of numbers) /2

Your first number is 2. Your last number is 2 x 100 = 200. The number of numbers in this series is 100 (says so in the question). So your sum equals:

(2 + 200) x 100 / 2 = 202 x 100 / 2 = 10100.

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Q: The sum of 100 even number starting with number 2?
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There are 25 prime numbers less than 100 is their sum even or odd?

The sum of the 25 primes less than 100 is even (it is 1060).The first prime number is 2. Every other prime number is odd.So, of the 25 primes less than 100, one is even and 24 are odd.Any two odd numbers sum to an even number. Therefore, an even number of odd numbers has an even sum. So the sum of 24 odd numbers is even.Therefore, the sum of the 25 primes less than 100 is even.


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