Question

2,12,72, ...

Arithmetic or Geometric
Common ratio or Common Difference
Linear or Exponential
Explicit Formula
Recursive Formula​

Answer 1

Geometric

Exponential

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

`a_n=6a_(n-1)` with
`a_1=2`

Explanation:

Arithmetic sequences have a common differences.

This is not arithmetic because 12-2 is not the same as 72-12. One is 10 while the other is 60.

Geometric sequences have a common ratio.

This is geometric because 12/2 is the same as 72/12. They are both 6.

Arithmetic sequences are linear.

Geometric sequence are exponential.

Since this is a geometric sequence, then is is exponential.

`a_1` means first term.

`a_(n-1)[tex] means the previous term to [tex]a_1`.

The arithmetic sequences have explicit form:
`a_n=a_1+d(n-1)`

The arithmetic sequences have recursive form:
`a_n=a_(n-1)+d` with
`a_1` given.

`d` represents the common difference.

The geometric sequences have explicit form:
`a_n=a_1(r)^(n-1)`

The geometric sequences have recursive form:
`a_n=r a_(n-1)` with
`a_1` given.

`r` is common ratio.

So since it geometric, then the explicit formula is
`a_n=2(6)^(n-1)` and the recursive form is
`a_n=6 a_(n-1)` with
`a_1=2`.