Answer:
[tex]a_{n}[/tex] = 10[tex](5)^{n-1}[/tex]
Step-by-step explanation:
Note that consecutive terms have a common ratio, that is
50 ÷ 10 = 250 ÷ 50 = 1250 ÷ 250 = 5
This indicates that the sequence is geometric with n th term ( explicit rule )
[tex]a_{n}[/tex] = a[tex](r)^{n-1}[/tex]
where a is the first term and r the common ratio,
Here a = 10 and r = 5, thus
[tex]a_{n}[/tex] = 10[tex](5)^{n-1}[/tex] ← explicit rule
