What is the nth term rule for this sequence?

Question

5,9,15,24,37
(please show method)

5,9,15,24,37
(please show method)
(in form of: an^3+bn^2+cn+d)

Answer 1

Take the differences of adjacent terms, then the differences of the differences, etc.:

5, 9, 15, 24, 37
4 (9-5), 6 (15-9), 9 (24-15), 13 (37-24)
2 (6-4), 3 (9-6), 4 (13-9)
1 (3-2), 1 (4-3)

The fourth term of the third series (differences of differences) should be 5, so the fifth term of the second series (differences) should be 13+5 = 18. And the sixth term of the original series should then be 37+18 = 55.

Getting a constant value in the third-level difference means that the series is represented by a third-degree equation, an^3 + bn^2 + cn + d

Answer 2

This appears to be a sequence whose third difference equals 1.

first difference: 4, 6, 9, 13, ...
second difference: 2, 3, 4, ...
third difference: 1, 1, ...

Therefore, the general sequence follows:

f(n) = f(n-1) + (f(n-1) - f(n-2)) + n
f(1) = 9
f(0) = 5

Answer 3

I can't do all of this but I can calculate the formula for the differences, maybe you can get a bit further from there.

The differences are calculated using (n^2 + n + 6) / 2

Sorry I can't do more !

Answer 4

check this out...The differences between 5,9,15,24,&37 are 4,6,9,&13. The differences between 4,6,9,&13 are 2,3,4,&5. So you know the next term is going to be 13+5+37