Answer:
Step-by-step explanation:
The given geometric sequence is:
2,6,18,54
Here, [tex]a_{1}=2[/tex], [tex]a_{2}=6[/tex], [tex]a_{3}=18[/tex] and [tex]a_{4}=54[/tex]
Explicit formula is given as: [tex]a_{n}=a_{1}r^{n-1}[/tex]
Now, [tex]r=\frac{a_{n+1}}{a_{n}}[/tex]
=[tex]\frac{6}{2}=3[/tex]
Substituting in the above explicit formula, we have
[tex]a_{n}=2(3)^{n-1}[/tex]
=[tex]2(3)^n(3)^{-1}=\frac{2}{3}(3)^n[/tex]
Recursive formula is given as:[tex]a_{1}=2[/tex], [tex]a_{n+1}=3a_{n}[/tex].
