Type the missing number in this sequence: 0, _____, 6, 12, 20, 30, 42, 56

Question

Type the missing number in this sequence:  0,    _____,    6,    12,    20,    30,    42,    56

Bytelearn · Accepted Answer

Identify Pattern: Identify the pattern in the sequence. The sequence given is: 0, ___, 6, 12, 20, 30, 42, 56. Let's look at the differences between the numbers: 6 - 0 = 6, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10, 42 - 30 = 12, 56 - 42 = 14. It seems that the difference between consecutive numbers is increasing by 2 each time.Determine Difference: Determine the difference between the first and second terms. Since the difference between the terms is increasing by 2, and the difference between the second and third terms is 6, the difference between the first and second terms should be 6 - 2 = 4.Calculate Missing Number: Calculate the missing number in the sequence. If the difference between the first term (0) and the missing number is 4, then the missing number is 0 + 4 = 4.Verify Pattern: Verify the pattern with the calculated missing number. Inserting the number 4 into the sequence: 0, 4, 6, 12, 20, 30, 42, 56. Now check the differences: 4 - 0 = 4, 6 - 4 = 2, 12 - 6 = 6, 20 - 12 = 8, 30 - 20 = 10, 42 - 30 = 12, 56 - 42 = 14. The differences are now: 4, 2, 6, 8, 10, 12, 14, which is not consistent with the pattern we identified. There is a mistake here.

Type the missing number in this sequence: $\newline$ $0$ , _____, $6$ , $12$ , $20$ , $30$ , $42$ , $56$

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Type the missing number in this sequence:\newline000, _____, 666, 121212, 202020, 303030, 424242, 565656

Type the missing number in this sequence: $\newline$ $0$ , _____, $6$ , $12$ , $20$ , $30$ , $42$ , $56$