Answer:
Step-by-step explanation:
The explicit formula of a geometric sequence:
[tex]a_n=a_1r^{n-1}[/tex]
1. We have
[tex]a_1=6,\ r=-8[/tex]
Substitute:
[tex]a_n=6\left(-8)^{n-1}[/tex]
Calculate the 7th term. Put n = 7:
[tex]a_7=6\cdot(-8)^{7-1}=6\cdot(-8)^6=6\cdot262,144=1,572,864[/tex]
2. We have
[tex]a_1=-3,\ r=\dfrac{1}{2}[/tex]
Substitute:
[tex]a_n=-3\cdot\left(\dfrac{1}{2}\right)^{n-1}[/tex]
Calculate the 6th term. Put n = 6:
[tex]a_6=-3\cdot\left(\dfrac{1}{2}\right)^{6-1}=-3\cdot\left(\dfrac{1}{2}\right)^5=-3\cdot\dfrac{1}{32}=-\dfrac{3}{32}[/tex]
3. We have
[tex]a_1=-0.25,\ r=-3[/tex]
Substitute:
[tex]a_n=-0.25\cdot(-3)^{n-1}[/tex]
Calculate the 10th term. Put n = 10:
[tex]a_{10}=-0.25\cdot(-3)^{10-1}=-0.25\cdot(-3)^9=-0.25\cdot(-19,683)=4,920.75[/tex]
