In a sequence of 200 numbers, every number (except the end ones) is sum of the two adjacent numbers in the sequence. If sum of all numbers is equal to the sum of first 100 numbers and the 35th number in the sequence is –6. Find the sum of the all numbers of given sequence.
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A triangular number or triangle number counts objects arranged in an equilateral triangle (thus triangular numbers are a type of figurate number, other examples being square numbers and cube numbers). The nth triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. The sequence of triangular numbers (sequence A000217 in the OEIS), starting at the 0th triangular number, is
The first six triangular numbers
0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 136, 153, 171, 190, 210, 231, 253, 276, 300, 325, 351, 378, 406, 435, 465, 496, 528, 561, 595, 630, 666...
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