Answer:
[tex]a_n=4^{n-1}[/tex]
Step-by-step explanation:
When each term is multiplied by a number to get the next term, it is a geometric sequence.
The general term (nth term) of a geometric sequence is given by the formula:
[tex]a_n=a_1*r^{n-1}[/tex]
Where [tex]a_1[/tex] is the first term and r is the common ratio (the number which is multiplied with a term to get the next term)
- It is given that the first term, [tex]a_1[/tex], is 1
- We also can figure out common ratio, r, to be 4 (since it is the number we multiply a term by, to get the next term)
Now plugging in these into the formula gives us:
[tex]a_n=a_1*r^{n-1}\\a_n=(1)*(4)^{n-1}\\a_n=4^{n-1}[/tex]
