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arithmetic sequences

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4 items are filed under this topic.
Finite differences 2003-02-10
From Jenny:

I need to find a formula that will work with any number.
I am finding the volume of a 3d cross- shape. Here are my results so far:

Term Number      0   1    2    3     4      5
nth term         1    7   25   63   129    231
1rst diff           6   18   38   66     102
2nd diff              12    20   28   36
3rd diff                  8     8    8

I can't seem to find a formula that will work with any number. Any help would be much appreciated.

Answered by Penny Nom.

Arithmetic sequences 2001-09-10
From Rachel:
I can't seem to figure out a problem that deals with arithmetic sequencing. This is the question: The 5th term in an arithmetic sequence is 1/2, and the 20th term is 7/8. Find the first three terms of the sequence. I attempted this problem with the formula: An = a + (n-1)d (where the n represents the nth term, a is the first term, and d represents the common difference) I keep getting -9.5 for the first number, and then 3/120 as the common difference between the numbers. But as I have figured it, the sequence is getting greater and greater, and my data does not go with the terms given.
Answered by Penny Nom.
Geometric and arithmetic sequences 2001-01-26
From Garry:
what are the equations for geometric and arithmetic sequences?

also, what are the equations for finding the sums of those series?

Answered by Leeanne Boehm and Penny Nom.
The sum of the squares of 13 consecutive positive integers 2000-08-25
From Wallace:
Prove that it is not possible to have the sum of the squares of 13 consecutive positive integers be a square.
Answered by Harley Weston.



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