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Given any set of k number it is easy to find a rule based on a polynomial of order 4+k such that the first five numbers are as listed in the question and the next k are the given numbers. That is, it is easy to find a rule so that any number can be the "next" in the sequence.

So, suppose you want the next two numbers to be (5, 15) again then you define the rule as

Un = (24n5 - 400n4 + 2460n3 - 6890n2 + 8736n - 3915)/3

The simplest polynomial rule is

Un = (20n3 - 90n2 + 160n - 75)/3

and according to that, the next three numbers are 325, 655, 1165.

Alternatively, you could go for a power sequence

Un = 5*3n-1 which implies the next three terms are 405, 1215, 3645.

An order 5 polynomial, order 3 polynomial, geometric progression (plus others). There is no objective way to choose between them.

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Q: What numbers come next 5 15 45 135?
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Related questions

What two numbers multiply to be 135 but add to be 6?

There are no such numbers but if you meant -135 then the numbers are -9 and 15


What are the next three numbers 5 15 45 135?

Each number is three times the previous number.


What is the LCM of numbers 15 and 27?

135


What numbers are divisible by 135?

Numbers such as 135, 270, 405, and other multiples of 135.


Can 7 go into 135?

No, but these numbers can: 1, 3, 5, 9, 15, 27, 45, 135.


Can 4 go into 135?

No, but these numbers can: 1, 3, 5, 9, 15, 27, 45, 135.


What two numbers have a GCF of 15 and a LCM of 270?

15 and 270 do.


What two whole numbers have the sum of 6 and a product of -135?

141


Can 75 go into 135?

No, just these numbers can: 1, 3, 5, 9, 15, 27, 45, 135.


Can 135 be divided by anything?

Yes, by these numbers: 1, 3, 5, 9, 15, 27, 45, 135,


What comes next in the sequence 5 15 45 135?

425


What do we multiply to get 135?

These numbers go evenly into 135: 1, 3, 5, 9, 15, 27, 45, 135.