Question

Write an explicit formula for a_na

n
​
, the n^{\text{th}}n
th
term of the sequence 18, 6, 2, ...

Answer 1

`a_(n)` = 18
`((1)/(3)) ^(n-1)`

Explanation:

there is a common ratio between consecutive terms, that is

`(6)/(18)` =
`(2)/(6)` =
`(1)/(3)`

this indicates the sequence is geometric with explicit formula

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = 18 and r =
`(1)/(3)` , then

`a_(n)` = 18
`((1)/(3)) ^(n-1)`