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Relevant wiki: Arithmetic Progressions
It is an arithmetic progression with a common difference of 3 . So the number of terms is 3 9 9 = 3 3 . And the desired sum is
x = 2 3 3 [ 2 ( 3 ) + ( 3 3 − 1 ) ( 3 ) ] = 1 6 8 3
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Since all of the numbers have a common factor of 3, we can re-write this sum as 3 ( 1 + 2 + 3 + . . . + 3 1 + 3 2 + 3 3 ) = x Now, we can just find the 33rd triangle number, which can be found using the formula: 3 ( 2 3 3 ( 3 3 + 1 ) ) This can be simplified to the expression of 9 9 × 1 7 which is equivalent to 1 , 6 8 3 .