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Question 1166128: Take a look at the sequence of square numbers listed in the first row of numbers
below. The first several terms of the sequence are listed and, below that, the first
differences of the two numbers immediately above, and below that are the
differences of the differences (i.e., the second differences).
1 4 9 16 25
3 5 7
2 2
9
2
2
36
11
2
13
2
Notice that for the sequence n2 the second differences are all 2.
2. Make a conjecture as to what will happen with the fourth powers and the fifth
powers. Make a conjecture about the differences and the resulting constant for
the sequence of kth powers of nk where k is a positive integer. [This Exploration
can be done by hand, or with a calculator, or in a spreadsheet program such as
Excel.]
3. If you are given a sequence of kth powers ank, is there a way to figure out the
value of the coefficient a?
I only need assistance with number 2 I included number 2 to help number 3 make better sense.
Answer by ikleyn(52782)   (Show Source):
You can put this solution on YOUR website! .
For n = 3, you can make your own experiment and to formulate your own conjecture then.
Try the third difference, in this case.
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