A sequence in arithmetic if any two pairs of succesive terms have the same common difference.

A sequence in geometric if any two pairs of succesive terms have the same common quotient (or ratio).

A) is geometric because 1÷(1/4) = 1×(4/1) = 4 and 4÷1 = 4 = common ratio = r

The formula for the nth term of a geometric sequence is:

 where  is the first term
and r is the common ratio:



So 

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B) is arithmetic because 7-2 = 5 and 12-7 = 5 = common difference = d

The formula for the nth term of an arithmetic sequence is:

 where  is the first term
and d is the common ratio:



So 

Edwin