Answer:
The 11th term is 3072.
Step-by-step explanation:
First, find the common ratio and the first term. The common ratio is 6/3 or 2. The first term is 3.
Use the direct formula, xi=a*r^i-1, to find the eleventh term. a is first term, and i is the index or the number of the term.
Substitute: x11=3*2^(11-1)
Or x11=3*2^10
So x11 is 3072
A geometric sequence is characterized by a common ratio. The 11th term of the geometric sequence is 3072
Given that:
[tex]Sequence= 3,6,12,24,[/tex]
First, we calculate the common ratio (r)
[tex]r = \frac{T_2}{T_1}[/tex]
Where:
[tex]T_2 = 6[/tex] --- the second term
[tex]T_1 = 3[/tex] --- the first term
So, we have:
[tex]r = \frac 63[/tex]
[tex]r = 2[/tex]
The nth term is calculated using:
[tex]T_n = T_1 \times r^{n-1}[/tex]
Where:
[tex]n = 11[/tex]
So, we have:
[tex]T_{11} = 3 \times 2^{11-1}[/tex]
[tex]T_{11} = 3 \times 2^{10}[/tex]
[tex]T_{11} = 3072[/tex]
Hence, the 11th term is 3072
Read more about geometric sequence at:
https://brainly.com/question/18109692
