Given:
The sequence is 2, 4, 8, 16,... .
To find:
The explicit formula for the sequence and use it to find the eleventh teen in the sequence.
Solution:
We have,
2, 4, 8, 16,...
It is a GP because the ratio between two consecutive terms are same..
Here,
First term: [tex]a = 2[/tex]
Common ratio: [tex]r=\dfrac{a_2}{a_}[/tex]
[tex]r=\dfrac{4}{2}[/tex]
[tex]r=2[/tex]
The explicit formula of GP is:
[tex]a_n=ar^{n-1}[/tex]
Putting [tex]a=2,r=2[/tex], we get
[tex]a_n=2(2)^{n-1}[/tex]
Put n=11 to find the 11th term of the given sequence.
[tex]a_{11}=2(2)^{11-1}[/tex]
[tex]a_{11}=2(2)^{10}[/tex]
[tex]a_{11}=2(1024)[/tex]
[tex]a_{11}=2048[/tex]
Therefore, the correct option is D.
