Question

Is the sequence geometric? If so, identify the common ratio. 6, 12, 24, 48,

Answer 1

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:

$a_1=6,\\\\a_2=12,\\\\a_3=24,\\\\a_4=48,\\\\etc.$

We can see that

$\dfrac{12}{6}=\dfrac{24}{12}=\dfrac{48}{24}=~.~.~.~=2,\\\\\Rightarrow \dfrac{a_2}{a_1}=\dfrac{a_3}{a_2}=\dfrac{a_4}{a_3}=~.~.~.~=2,\\\\\Rightarrow a_2=2\times a_1,~~a_3=2\times a_2,~~a_4=2\times a_3,~.~.~.etc.$

Therefore, each term is formed by multiplying 2 to the preceding term.

Thus, the given sequence is a geometric sequence with common ratio 2.

Answer 2

Yes
common ratio= r2/r1 or r3/r2 or r4/r3 if it is all the same then it is a geometric sequence, so the common ratio is 2 because 12/6=2, 24/12=2 and 48/24=2