SOLUTION: if f (1) = 6 and f (n)= f (n-1) + 2 then find the value of f (4)

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Question 1191041: if f (1) = 6 and f (n)= f (n-1) + 2 then find the value of f (4)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Let the place count be n
Let the nth term be a%5Bn%5D
Given f%28n=1%29=6
We are also told that any one term is the previous term + 2.
This is derived from f%28n%29=f%28n-1%29%2B2 where f%28n-1%29+is the previous term.
Consequently we have an Arithmetic sequence with common difference of +2
From this the sequence is:
n=1→a%5B1%5D=6← given value
n=2→a%5B2%5D=6%2B2=8
n=3→a%5B3%5D=6%2B2%2B2=10
highlight%28n=4%29→highlight%28a%5B4%5D=6%2B2%2B2%2B2=12%29

so, the value of highlight%28f%284%29%29 is highlight%2812%29

And so on. Also from this we also have an alternative equation for any an in that we have:
a%5Bn%5D=6%2B2%28n-1%29