1, 4, 14, 45 What's The Next Number?


2 Answers

d ds Profile
d ds answered
Series would be like: 1, 4, 14, 45, 139.

It is like that:


4     [(1*3) + 1]

14   [(4*3) + 2]

45   [(14*3)+3]

139 [(45*3)+4]

Logic: You need to a Multiply the previous number with three and add
the digit that comes next to previously added number as shown above.
thanked the writer.
Oddman commented
Helpful has shown you a series that is essentially exponential. The series could be polynomial, in which case the next number might be 111. Take differences of the numbers given, then differences of those. First differences: 3, 10, 31. Second differences: 7, 21. If the second differences continue in the same fashion (arithmetically), then next second difference might be 35 (=21+14). Then the next first difference would be 66 = 31+35. Then the next number in the sequence would be 111 = 45 + 66.

What Helpful has done is say of the second differences that they differ by a factor of 3, and that the next second difference should be 63 = 21*3. So then the next first difference would be 94 = 31+63, and the next sequence number would be 139 = 45+94.

You have to decide in the context in which the problem is given whether the sequence is expected to be polynomial or exponential (or something else). The trouble with this sort of question on a quiz is that there are multiple "right" answers, depending on the rule you choose for getting from one sequence element to the next.

You could reasonably argue, for example that the next element should be 149, where the 14 comes from the element 2 before, and the 9 comes from the sum of the digits of the element 1 before. This rule matches both of the elements after the first two in the series. 14 = 1|4; 45 = 4|(1+4).

A quiz author will usually justify the "right" answer by saying they are looking for the simplest rule. Arguably, a polynomial rule is simpler than an exponential rule, but a "copy digits, sum digits" rule might arguably be simpler yet. Therein lies the problem with "next in sequence" questions.

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