Question

Which of the following is a geometric sequence?A. 3, 6, 12, 24,...B. 2, 7, 12, 17, ...C. 34, 35, 38, 43, ...D. 1, 4, 9, 16, ...

Answer 1

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

`a_1,a_1+1,(a_1+1)+3_{}`

Which is an arithmetic sequence and not a geometric one.

As for B, we can see that the sequence is simply

`a_n=a_(n-1)+5_{}`

Which is another arithmetic sequence.

Finally, in the case of option A, the sequence has the form:

`\begin{gathered} a_n=2a_(n-1) \\ a_0=3 \end{gathered}`

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