Sum

Algebra Level 2

Find the sum of all the numbers between 0 0 and 20000 20000 which is divisible by 99 99 .


The answer is 2029797.

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1 solution

The sequence of numbers forms an arithmetic progression with a common difference of d = 99 d=99 .

The number of terms is n = 20000 99 = 202 n=\dfrac{20000}{99}=202 . The last term is a 202 = 99 ( 202 ) = 19998 a_{202}=99(202)=19998 . The first term is a 1 = 99 a_1=99 . So the terms are ( 99 , 198 , 297...19998 ) (99,198,297...19998) .

By using the formula for the sum, we get

s = n 2 ( a 1 + a 202 ) = 202 2 ( 99 + 19998 ) = 2029797 s=\dfrac{n}{2} \left(a_1+a_{202} \right)=\dfrac{202}{2}(99+19998)=2029797

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