Answer:
[tex]a_7=40960x^{33}[/tex]
Step-by-step explanation:
Geometric sequence has explicit form:
[tex]a_n=a \cdot r^{n-1}[/tex] where [tex]a[/tex] is first term and [tex]r[/tex] is the common ratio.
First term here is [tex]a=10x^3[/tex] and [tex]r[/tex] could be found by doing second term divided by first term, [tex]\frac{40x^8}{10x^3}=4x^5[/tex].
Therefore the [tex]n[/tex]th term is given by
[tex]a_n=10x^3 \cdot (4x^5)^{n-1}[/tex].
So the [tex]7[/tex]th term is given by
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex].
Let's simplify:
[tex]a_7=10x^3 \cdot (4x^5)^{7-1}[/tex]
[tex]a_7=10x^3 \cdot (4x^5)^{6}[/tex]
[tex]a_7=10x^3 \cdot (4^6(x^5)^6)[/tex]
[tex]a_7=10x^3 \cdot (4096x^30)[/tex]
[tex]a_7=40960x^{33}[/tex]
