Question

2,12,72, ...
Arithmetic or Geometric
Common ratio or Common Difference
Linear or Exponential
Explicit Formula
Recursive Formula​

Answer 1

Answer:

Geometric

Exponential

$a_n=2(6)^{n-1}$

$a_n=6a_{n-1}$ with $a_1=2$

Step-by-step 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 $a_1=2$.