Which of the following numbers will replace the question mark (?) in the given series?
29, 30, 26, 35, 19, ?
Correct Answer :
44
Solution :
The correct answer is 44.
To find the missing number in the series, let us analyze the differences between consecutive terms:
First term to second term: 30 - 29 = +1 (which is +12)
Second term to third term: 26 - 30 = -4 (which is -22)
Third term to fourth term: 35 - 26 = +9 (which is +32)
Fourth term to fifth term: 19 - 35 = -16 (which is -42)
The pattern shows that the differences are alternating in sign (+, -, +, -, ...) and are the squares of consecutive positive integers (12, 22, 32, 42, ...).
Following this pattern, the next difference should be:
Adding this difference to the fifth term (19) gives the next number in the series:
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