Question

Write a recursive definition for the sequence 14, 10, 6, 2...

Answer 1

The answer is:

d. $a_{1}=14,$ $a_{n}=a_{n-1}-4$

Answer 2

The general form of recursive definition for arithmetic sequence:
$a_{n}=a_{1}+d(n-1)$

So, what we need to do is to find $a_{1}$ and $d$.
$a_{1}=14$
$d=a_{2}-a_{1}=10-14=-4$
Having found these two values we can now define our recursive sequence:
$a_{n}=14-4(n-1)$
$a_{n}=14-4n+4$
$a_{n}=18-4n$