Answer:
The given sequence is a geometric sequence and the common ratio is 4
Step-by-step explanation:
A geometric sequence is a sequence in which the next term is obtained by multiplying the previous term with a ratio r.
Given sequence is:
6,24,96,384,1536,…
Here
a1 = 6
a2 = 24
a3 = 96
a4 = 384
a5 = 1536
The common ratio is the ratio between consecutive terms of a geometric sequence.
If the common ratio of a sequence is same, then the sequence is a geometric sequence.
So,
[tex]r = \frac{a_2}{a_1} = \frac{24}{6} = 4\\r = \frac{a_3}{a_2} = \frac{96}{24} = 4\\r = \frac{a_4}{a_3} = \frac{384}{96} = 4\\r = \frac{a_5}{a_4} = \frac{1536}{384}= 4[/tex]
As the common ratio is same, the given sequence is a geometric sequence.
Hence,
The given sequence is a geometric sequence and the common ratio is 4
