Answer:
3072
Step-by-step explanation:
General form of a geometric sequence:
[tex]a_n=ar^{n-1}[/tex]
where:
- [tex]a_n[/tex] is the nth term
- a is the first term
- r is the common ratio
Given values:
- first term, a = 3
- common ratio, r = 4
Substitute the given values into the formula to create an equation for the nth term:
[tex]\implies a_n=3(4)^{n-1}[/tex]
To find the 6th term, substitute n = 6 into the equation:
[tex]\implies a_6=3(4)^{6-1}[/tex]
[tex]\implies a_6=3(4)^{5}[/tex]
[tex]\implies a_6=3(1024)[/tex]
[tex]\implies a_6=3072[/tex]
Therefore, the 6th term of a geometric sequence whose 1st term is 3 and whose common ratio is 4 is 3072.
Learn more about geometric sequences here:
https://brainly.com/question/27783194
