SOLUTION: For the sequence 2, 9, 28, 65,... How do I find the next term and the rule for the nth term

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Question 868395: For the sequence 2, 9, 28, 65,... How do I find the next term and the rule for the nth term
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%28n%5E3+%2B+1%29 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%5E3+%2B+1+=+3%5E3+%2B+1+=+27+%2B+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%5E3+%2B+1+=+5%5E3+%2B+1+=+125+%2B+1+=+highlight%28126%29


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