Answer:
[tex]\dfrac{1}{216}[/tex] = 0.005 (nearest thousandth)
Step-by-step explanation:
geometric series formula: [tex]a_n=ar^{n-1}[/tex]
where a is the first term and r is the common ratio
Given:
- [tex]a_1=216[/tex]
- [tex]a_2=36[/tex]
- [tex]a_3=6[/tex]
[tex]r=\dfrac{a_2}{a_1}=\dfrac{36}{216}=\dfrac16[/tex]
[tex]\implies a_n=216 \cdot \dfrac16^{n-1}[/tex]
[tex]\implies a_7=216 \cdot \dfrac16^{7-1}=\dfrac{1}{216}=0.005[/tex]
