Answer:
see explanation
Step-by-step explanation:
There is a common ratio r between consecutive terms, that is
[tex]\frac{a_{2} }{a_{1} }[/tex] = [tex]\frac{75}{25}[/tex] = 3
[tex]\frac{a_{3} }{a_{2} }[/tex] = [tex]\frac{225}{75}[/tex] = 3
[tex]\frac{a_{4} }{a_{3} }[/tex] = [tex]\frac{675}{225}[/tex] = 3
This indicates the sequence is geometric with explicit formula
[tex]a_{n}[/tex] = a₁ [tex](r)^{n-1}[/tex]
where a₁ is the first term and r the common ratio
Here a₁ = 25 and r = 3 , then
a₆ = 25 × [tex]3^{5}[/tex] = 25 × 243 = 6075
