Question

( g(1) = 14
(g(n) = g(n − 1) – 4
Find an explicit formula for g(n).
g(n) =

Answer 1

18-4n

Explanation:

Answer 2

`g(n)=18-4n`

Explanation:

You are given the function g, for which

`g(1)=14,\\\\g(n)=g(n-1)-4`

Find some values of this function:

`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\\ \\...`

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

`a_n=a_1+(n-1)d,`

where

`a_1=g(1)=14\\ \\d=-4`

So,

`g(n)=a_n=14+(n-1)\cdot (-4)=14-4n+4=18-4n`