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3 years ago

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

Mathematics

1 answer:

I am Lyosha [343]3 years ago

3 0

Answer:

$g(n)=18-4n$

Step-by-step 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,

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

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Answer:

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Step-by-step explanation:

<em>First method: Logical thinking</em>

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