Given:
The sequence can be generated by
[tex]a_n=4a_{(n - 1)}[/tex]
Where [tex]a_1= 6[/tex] and [tex]n[/tex] is a whole number greater than 1.
To find:
The first four terms of the given sequence.
Solution:
We have,
[tex]a_n=4a_{(n - 1)}[/tex] ...(i)
It is given that [tex]a_1= 6[/tex]. So, for [tex]n=2[/tex], we get
[tex]a_2=4a_{(2 - 1)}[/tex]
[tex]a_2=4a_1[/tex]
[tex]a_2=4(6)[/tex]
[tex]a_2=24[/tex]
Putting [tex]n=3[/tex] in (i), we get
[tex]a_3=4a_{(3- 1)}[/tex]
[tex]a_3=4a_2[/tex]
[tex]a_3=4(24)[/tex]
[tex]a_3=96[/tex]
Putting [tex]n=4[/tex] in (i), we get
[tex]a_4=4a_{(4- 1)}[/tex]
[tex]a_4=4a_3[/tex]
[tex]a_4=4(96)[/tex]
[tex]a_4=384[/tex]
The first four terms of the given sequence are 6, 24, 96,384.
Therefore, the correct option is C.
