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Type the missing number in this sequence:\newline00, _____, 66, 1212, 2020, 3030, 4242, 5656

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Full solution

Q. Type the missing number in this sequence:\newline00, _____, 66, 1212, 2020, 3030, 4242, 5656
  1. Identify Pattern: Identify the pattern in the sequence.\newlineThe sequence given is: 00, ___, 66, 1212, 2020, 3030, 4242, 5656.\newlineLet's look at the differences between the numbers: 6−0=66 - 0 = 6, 12−6=612 - 6 = 6, 20−12=820 - 12 = 8, 6600, 6611, 6622.\newlineIt seems that the difference between consecutive numbers is increasing by 6633 each time.
  2. Determine Difference: Determine the difference between the first and second terms.\newlineSince the difference between the terms is increasing by 22, and the difference between the second and third terms is 66, the difference between the first and second terms should be 6−2=46 - 2 = 4.
  3. Calculate Missing Number: Calculate the missing number in the sequence.\newlineIf the difference between the first term 00 and the missing number is 44, then the missing number is 0+4=40 + 4 = 4.
  4. Verify Pattern: Verify the pattern with the calculated missing number.\newlineInserting the number 44 into the sequence: 0,4,6,12,20,30,42,560, 4, 6, 12, 20, 30, 42, 56.\newlineNow check the differences: 4−0=44 - 0 = 4, 6−4=26 - 4 = 2, 12−6=612 - 6 = 6, 20−12=820 - 12 = 8, 30−20=1030 - 20 = 10, 42−30=1242 - 30 = 12, 56−42=1456 - 42 = 14.\newlineThe differences are now: 4,2,6,8,10,12,144, 2, 6, 8, 10, 12, 14, which is not consistent with the pattern we identified. There is a mistake here.

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