Answer: Yes, the given sequence is geometric with common ration 2.
Step-by-step explanation: The given sequence is:
6, 12, 24, 48, . . ..
We are to check whether the above sequence is geometric or not. If it is geometric, we are to find the common ratio.
Geometric sequence - a sequence of numbers where each term is found by multiplying by a constant to the preceding term. This constant is called the common ratio, r.
The consecutive terms of the given sequence can be written as:
[tex]a_1=6,\\\\a_2=12,\\\\a_3=24,\\\\a_4=48,\\\\etc.[/tex]
We can see that
[tex]\dfrac{12}{6}=\dfrac{24}{12}=\dfrac{48}{24}=~.~.~.~=2,\\\\\Rightarrow \dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=~.~.~.~=2,\\\\\Rightarrow a_2=2\times a_1,~~a_3=2\times a_2,~~a_4=2\times a_3,~.~.~.etc.[/tex]
Therefore, each term is formed by multiplying 2 to the preceding term.
Thus, the given sequence is a geometric sequence with common ratio 2.
