The 11th term of the sequence is [tex]a_{11}=2048[/tex]
Explanation:
The sequence is [tex]2,4,8,16[/tex]
We need to find the 11th term of the sequence.
First, let us determine the common ratio of the sequence.
[tex]r=\frac{4}{2} =2[/tex]
[tex]r=\frac{8}{4} =2[/tex]
[tex]r=\frac{16}{8} =2[/tex]
Thus, the common ratio of the sequence is [tex]r=2[/tex]
Since, the sequence follows geometric progression.
The general formula for GP is
[tex]a_n=ar^{n-1}[/tex]
Substituting [tex]n=11[/tex], [tex]r=2[/tex] and [tex]a=1[/tex] we have,
[tex]a_{11}=2(2)^{11-1}[/tex]
[tex]=2(2)^{10}[/tex]
[tex]=2(1024)[/tex]
[tex]=2048[/tex]
Thus, the 11th term of the sequence is [tex]a_{11}=2048[/tex]
