The sequence 3, 12, 48, 192 is classified as which type?

The sequence 3, 12, 48, 192 can be classified as a geometric sequence because each term is obtained by multiplying the previous term by a constant factor.

To examine this more specifically, observe how to get from one term to the next:

• From 3 to 12, you multiply by 4 (3 × 4 = 12).

• From 12 to 48, you again multiply by 4 (12 × 4 = 48).

• From 48 to 192, you continue the pattern by multiplying by 4 (48 × 4 = 192).

Since each term is produced by consistently multiplying the preceding term by the same value (in this case, 4), this confirms that the sequence is geometric. The first term is 3, and with each step, you consistently apply the same multiplication factor, which is the defining characteristic of a geometric sequence.

In contrast, an arithmetic sequence would require adding or subtracting a constant value, neither of which applies here. The other classifications, “neither” and “harmonic,” do not fit the behavior of this sequence, as harmonic sequences involve terms being the reciprocals of an arithmetic sequence, which does not apply in this