SOLUTION: is the sequence 2, 6, 12, 20 arithmetic, geometric, or neither?

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Question 897665: is the sequence 2, 6, 12, 20 arithmetic, geometric, or neither?
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
2, 6, 12, 20
Let's test it to see if it is arithmetic sequence:

(2nd term) - (1st term) = 6 - 2 = 4

(3rd term) - (2nd term) = 12 - 6 = 6  

The test fails.  4 and 6 aren't the same.  To be an arithmetic sequence,
any term subtracted from the next term must always give the same number,
called the common difference.  So it is not an arithmetic sequence, because
4 and 6 are different.

Let's test it to see if it is geometric sequence:

matrix%281%2C2%2C2nd%2Cterm%29%2Fmatrix%281%2C2%2C1st%2Cterm%29%22%22=%22%226%2F2%22%22=%22%223

matrix%281%2C2%2C3rd%2Cterm%29%2Fmatrix%281%2C2%2C2nd%2Cterm%29%22%22=%22%2212%2F6%22%22=%22%222

The test fails also.  They aren't the same.  To be an geometric sequence,
any term divided be the preceding term must always give the same number,
called the common ratio.  So it is not a geometric sequence either.

It is neither an arithmetic nor a geometric sequence.

Edwin