A geometric sequence is a list of number in which each term after the first is found by multiplying the previous one by a constant (called the common ratio)
So, we can study case by case and check in which option this definition applies
At first, we can notice that D is the sequence n^2, which is not a geometric sequence
As for C, we can see that this sequence is
[tex]a_1,a_1+1,(a_1+1)+3_{}[/tex]
Which is an arithmetic sequence and not a geometric one.
As for B, we can see that the sequence is simply
[tex]a_n=a_{n-1}+5_{}[/tex]
Which is another arithmetic sequence.
Finally, in the case of option A, the sequence has the form:
[tex]\begin{gathered} a_n=2a_{n-1} \\ a_0=3 \end{gathered}[/tex]
Which is a geometric sequence as we found that the common ratio is equal to 2 and the initial value of the sequence is 3.
Therefore, the answer is option A
