Question

The first four terms of a sequence are \text{3, -6, 12, -24}. Write an explicit formula for this sequence, where n is any term number and a\left(n\right) is the nth term

Answer 1

see explanation

Explanation:

The terms form a geometric sequence with n th term

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

where a is the first term and r the common ratio

r =
`(a_(2) )/(a_(1) )` =
`(a_(3) )/(a_(2) )` = ......

r =
`(-6)/(3)` =
`(12)/(-6)` = - 2 and a = 3, hence

`a_(n)` = 3
`(-2)^(n-1)` ← explicit formula