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------------------------------------------------ Type the missing number in this sequence: 67, 70, 83, __, 139, 182, 235.

Answer :

Final answer:

The missing number in the sequence 67, 70, 83, 139, 182, 235 is 290. The differences between numbers follow a pattern related to subsequent prime numbers, leading to the next difference being +55, and thus the next number being 290.

Explanation:

The missing number in the sequence 67, 70, 83, 139, 182, 235 is 108. To find the missing number, observe the pattern of differences between consecutive terms. The sequence of differences is: +3, +13, +56, +43, +53, which doesn't exhibit an immediately recognizable pattern.

However, inspecting them closely, the differences themselves form a pattern: after the first difference of +3, each difference is a multiple of the previous prime number. Therefore, we add 2 (which is the next prime number after the starting difference of 3) to 53 to get the next difference of +55. Adding 55 to the last term, 235, gives us 235 + 55 = 290. The complete sequence is 67, 70, 83, 139, 182, 235, 290.