x?

Algebra Level 1

Find x x .

7 + 14 + 21 + . . . + 5999 = x \large{7+14+21+...+5999=x}


The answer is 2573571.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

Relevant wiki: Arithmetic Progressions

It is an arithmetic progression with a common difference of 7 7 . So the number of terms is 5999 7 = 857 \dfrac{5999}{7}=857 . And the desired sum is

x = 857 2 [ 2 ( 7 ) + ( 857 − 1 ) ( 7 ) ] = 2573571 x=\dfrac{857}{2}[2(7)+(857-1)(7)]=\boxed{2573571}

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