Question

What is the explicit formula for the sequence that is associated with the table?

Answer 1

see explanation

Explanation:

Consider the values of y

`(2)/(5)`, 2, 10, 50

Consider the ratio between consecutive terms

2 ÷
`(2)/(5)` = 5

10 ÷ 2 = 5

50 ÷ 10 = 5

Since the ratio is common then the terms form a geometric sequence

The n th term of a geometric sequence is

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

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

`a_(n)` =
`(2)/(5)`
`(5)^(n-1)` ← explicit formula