## anonymous one year ago A sequence is defined by the formula f(n + 1) = f(n) – 3. If f(4) = 22, what is f(1)?

1. SolomonZelman

the part f(n+1)=f(n)-3 tells us that the common defference is d=3. Then, we are given that f(4)=22. So this is what we can do: We know a formula for any nth term in arithmetic sequence (this sequence is also arithmetic): $$a_n=a_1+{\rm d}(n-1)$$ Now, for 4th term, it would be: $$a_4=a_1+{\rm d}(4-1)$$ $$a_4=a_1+3{\rm d}$$ Then you know that$$a_4=22$$ and d=-3 So, $$22=a_1+3{\rm (-3)}$$

2. SolomonZelman

So solve for $$a_1$$. (apologize for going from notation of f(n) to $$a_n$$, and hope that is ok:) )

3. anonymous

It's fine and is the answer 31? I'm going to add this is my notes!

4. SolomonZelman

$$22=a_1+3(-3)$$ $$22=a_1-9$$ $$31=a_1$$ yes, 31 is correct.

5. SolomonZelman

I apologize, I had to depart (buying stuff at home depot for fuuture further bath constructions)