Step-by-step explanation:
Given,
First term (a) = 6, common ratio (r) = [tex]4x^3[/tex] , number of terms (n) = 6
To find, the 6th term of the geometric sequence [tex](a_{6})=?[/tex]
Using an explicit formula for the sequence,
The nth term of the geometric sequence,
[tex]a_{n} =ar^{n-1}[/tex]
∴ The 6th term of the geometric sequence,
[tex]a_{6} =4(4x^3)^{6-1}[/tex]
⇒ [tex]a_{6} =4(4x^3)^{5}[/tex]
⇒ [tex]a_{6} =4(4^5)x^{3\times 5}[/tex]
⇒ [tex]a_{6} =4^{5+1}x^{15}[/tex]
⇒ [tex]a_{6} =4^{6}x^{15}[/tex]
Thus, the 6th term of the geometric sequence, [tex]a_{6} =4^{6}x^{15}[/tex].
