Question

Determine the explicit formula of the following sequence -3,-18,-108...

Answer 1

`a_(n)` = - 3
`(6)^(n-1)`

Explanation:

Note the common ratio r between consecutive terms, that is

r = - 18 ÷ - 3 = - 108 ÷ - 18 = 6

This indicates the sequence is geometric with n th term ( explicit formula )

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

where a is the first term and r the common ratio

Here a = - 3 and r = 6, thus

`a_(n)` = - 3
`(6)^(n-1)`