Which describes the difference between the two sequences? first sequence: 3, 6, 9, 12, second sequence: 3, 12, 48, 192, the first sequence is geometric because there is a common difference of 3. the second sequence is arithmetic because there is a common ratio of 4. the first sequence is arithmetic because there is a common difference of 3. the second sequence is geometric because there is a common ratio of 4. the first sequence is arithmetic because there is a common ratio of 3. the second sequence is geometric because there is a common difference of 4. the first sequence is arithmetic because there is a common difference of 4. the second sequence is geometric because there is a common ratio of 3.

The first sequence is arithmetic because there is a common difference of 3. The second sequence is geometric because there is a common ratio of 4.

Arithmetic sequence--

A sequence is said to be a arithmetic sequence if the difference of each term of the sequence with it's preceding term is constant.

This fixed constant is called as a common difference and is denoted by d.

i.e.

where is the nth term of the sequence.

Geometric sequence--

A sequence is said to be a geometric sequence if each term of the sequence is a constant multiple of the preceding term of the sequence.

The constant is known as the common ratio and is denoted by r.

i.e.

First Sequence:   3, 6, 9, 12, ...

By looking at the sequence we have:

Hence, this sequence is an arithmetic sequence with a common difference of 3.

Second Sequence:    3, 12, 48, 192, ...

By looking at the sequence we have:

and

Also,

Hence, this sequence is an geometric sequence with a common ratio of 4.

yes

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