SOLUTION: Is 12,40,68,96 sequence geometric or arthmetic? If possible what is the common ratio or difference

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Question 736363: Is 12,40,68,96 sequence geometric or arthmetic? If possible what is the common ratio or difference

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
For arithmetic sequences, the common difference is d, and the first term a%5B1%5D is often referred to simply as "a". Since you get the next term by adding the common difference, the value of a%5B2%5D is just a+%2B+d. The third term is a%5B3%5D+=+%28a+%2B+d%29+%2B+d+=+a+%2B+2d. The fourth term is a%5B4%5D+=+%28a+%2B+2d%29+%2B+d+=+a+%2B+3d. Following this pattern, the n-th term an will have the form
a%5Bn%5D+=+a+%2B+d%28n+-1%29.
For geometric sequences, the common ratio is r, and the first term a%5B1%5D is often referred to simply as "a". Since you get the next term by multiplying by the common ratio, the value of a%5B2%5D is just ar. The third term is a%5B3%5D+=+r%28ar%29+=+ar%5E2. The fourth term is a%5B4%5D+=+r%28ar%5E2%29+=+ar%5E3. Following this pattern, the n-th term an will have the form
a%5Bn%5D+=+ar%5E%28n+-1%29.
in your case 12,40,68,96 sequence is have the form
common difference is 28 and the greatest common divisor is 4
first term is 12 and if divided by 4, we get 3 that could be written as 7n-4 starting with n=1 and up

so, the recursive formula is:
a%5Bn%5D=4%287n-4%29
and this is arithmetic sequence