Answer:
[tex]g(n)=18-4n[/tex]
Step-by-step explanation:
You are given the function g, for which
[tex]g(1)=14,\\\\g(n)=g(n-1)-4[/tex]
Find some values of this function:
[tex]g(1)=14\\ \\g(2)=g(2-1)-4=g(1)-4=14-4=10\\ \\g(3)=g(3-1)-4=g(2)-4=10-4=6\\ \\g(4)=g(4-1)-4=g(3)-4=6-4=2\\ \\...[/tex]
You can see that ecah next value is 4 less than previous one, so these values form an arithmetic sequence and you have to find the nth term of this sequence. The nth term of arithmetic sequence is
[tex]a_n=a_1+(n-1)d,[/tex]
where
[tex]a_1=g(1)=14\\ \\d=-4[/tex]
So,
[tex]g(n)=a_n=14+(n-1)\cdot (-4)=14-4n+4=18-4n[/tex]
