Answer:
[tex]7x^{25}[/tex]
Step-by-step explanation:
Given sequence: [tex]7x, -7x^5, 7x^9[/tex]
General form of a geometric sequence: [tex]a_n=ar^{n-1}[/tex]
(where a is the first term and r is the common ratio)
[tex]a_1=7x[/tex]
[tex]a_2=-7x^5[/tex]
[tex]a_3=7x^9[/tex]
To find the common ratio, divide one term by the previous term:
[tex]r=\dfrac{a_2}{a_1}=\dfrac{-7x^5}{7x}=-x^4[/tex]
Therefore, substituting the found values of a and r into the formula:
[tex]\implies a_n=(7x)(-x^4)^{n-1}[/tex]
To find the 7th term, substitute n = 7 into the formula:
[tex]\begin{aligned}\implies a_7 & =(7x)(-x^4)^{7-1}\\ & = (7x)(-x^4)^6\\ & = (7x)(x^{24})\\ & = 7x^{25}\end{aligned}[/tex]
