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

Question

solomonzelman · Answer

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,
$22=a_1+3{\rm (-3)}$

solomonzelman · Answer

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

anonymous · Answer

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

solomonzelman · Answer

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

solomonzelman · Answer

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