Given:
The sequence is
1, 4, 16, 64
To find:
The general term of the given sequence.
Solution:
We have, the sequence
1, 4, 16, 64
Here, the ratio between two consecutive terms is same. So, it is a geometric sequence.
First term is:
[tex]a=1[/tex]
Common ratio is:
[tex]r=\dfrac{a_2}{a_1}[/tex]
[tex]r=\dfrac{4}{1}[/tex]
[tex]r=4[/tex]
The nth term of a geometric sequence is
[tex]a_n=ar^{n-1}[/tex] ...(i)
Where, a is the first term and r is the common ratio.
Putting a=1 and r=4 in (i), we get
[tex]a_n=(1)(4)^{n-1}[/tex]
[tex]a_n=4^{n-1}[/tex]
Therefore, the general term of the given sequence is [tex]a_n=4^{n-1}[/tex].
