Answer:
[tex]a_7=\dfrac{4}{729}[/tex]
Step-by-step explanation:
General form of geometric progression: [tex]a_n=ar^{n-1}[/tex]
(where [tex]a[/tex] is the initial term and [tex]r[/tex] is the common ratio)
Given:
- [tex]a=4[/tex]
- [tex]r=\dfrac13[/tex]
[tex]\implies a_n=4\left(\dfrac13\right)^{n-1}[/tex]
Therefore, when n = 7:
[tex]\implies a_7=4\left(\dfrac13\right)^{7-1}[/tex]
[tex]\implies a_7=4\left(\dfrac13\right)^{6}[/tex]
[tex]\implies a_7=4\left(\dfrac{1^6}{3^6}\right)[/tex]
[tex]\implies a_7=4\left(\dfrac{1}{729}\right)[/tex]
[tex]\implies a_7=\dfrac{4}{729}[/tex]
