Question

How do I write an explicit rule for this sequence?

Answer 1

`a_(n)` = 10
`(5)^(n-1)`

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 )

`a_(n)` = a
`(r)^(n-1)`

where a is the first term and r the common ratio,

Here a = 10 and r = 5, thus

`a_(n)` = 10
`(5)^(n-1)` ← explicit rule

Answer 2

next should be 2250 if my math is correct