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Question 1166133: 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 36 49 64 81...
3 5 7 9 11 13 15 17...
2 2 2 2 2 2 2...
Notice that for the sequence n^2 the second differences are all 2.
*I need help with only number 3 I just put number 2 for the question to make more since*
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 n^k 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 an^k, is there a way to figure out the value of the coefficient a?
Answer by ikleyn(52787)   (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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