Question 868395
Subtract 1 from each term to get 


2-1 = 1
9-1 = 8
28-1 = 27
65-1 = 64



Each number on the right hand side (RHS) is a perfect cube


1 = 1^3
8 = 2^3
27 = 3^3
64 = 4^3



So the rule is "cube the number, then add 1". We add 1 to undo the subtraction of 1 we did in the first part (see above)



So the rule is {{{highlight(n^3 + 1)}}} where n is a positive whole number.



Once you get the general rule or formula, it's always a good idea to test it with the given sequence you already have. For instance, the third term is given to be 28. So if we did things right, then plugging n = 3 into the formula should give 28. Since {{{n^3 + 1 = 3^3 + 1 = 27 + 1 = 28}}}, this example confirms it. I recommend testing the other remaining terms.



The next term would be when {{{n = 5}}}, so the next term is {{{n^3 + 1 = 5^3 + 1 = 125 + 1 = highlight(126)}}}



Note: you can do each part in any order, but I find it easier to find the general rule/formula first.