Question

Write an explicit formula for an, the nth term of the sequence 6, 12, 24, ....

Answer 1

`a_(n)` = 6
`(2)^(n-1)`

Explanation:

there is a common ratio between consecutive terms, that is

`(12)/(6)` =
`(24)/(12)` = 2

this indicates the sequence is geometric with nth term

`a_(n)` = a₁
`(r)^(n-1)`

where a₁ is the first term and r the common ratio

here a₁ = 6 and r = 2 , then

`a_(n)` = 6
`(2)^(n-1)`