anonymous
  • anonymous
A sequence is defined by the formula f(n + 1) = f(n) – 3. If f(4) = 22, what is f(1)?
Mathematics
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SOLVED
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jamiebookeater
  • jamiebookeater
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SolomonZelman
  • 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, \(22=a_1+3{\rm (-3)}\)
SolomonZelman
  • SolomonZelman
So solve for \(a_1\). (apologize for going from notation of f(n) to \(a_n\), and hope that is ok:) )
anonymous
  • anonymous
It's fine and is the answer 31? I'm going to add this is my notes!

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SolomonZelman
  • SolomonZelman
\(22=a_1+3(-3)\) \(22=a_1-9\) \(31=a_1\) yes, 31 is correct.
SolomonZelman
  • SolomonZelman
I apologize, I had to depart (buying stuff at home depot for fuuture further bath constructions)

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