Is - 3,12,-48 ... a arithmetic or geometric formula

geometric sequence

Step-by-step explanation:

A list of 3 numbers is not a "formula". It is a "sequence."

The differences between the numbers are ...

12 - (-3) = 15

-48 - 12 = - 60

These are not constant, so the sequence is not arithmetic.

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The ratios between the numbers are ...

12/-3 = - 4

-48/12 = - 4

These are constant, so the sequence is geometric.

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The formula for the n-th term of a geometric sequence is ...

an = a1·r^ (n-1)

We have first term a1 = - 3 and common ratio r = - 4. So, the formula for this sequence is ...

an = - 3 (-4) ^ (n-1)