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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)?
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)?

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SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1the 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): \(a_n=a_1+{\rm d}(n1)\) Now, for 4th term, it would be: \(a_4=a_1+{\rm d}(41)\) \(a_4=a_1+3{\rm d}\) Then you know that\(a_4=22\) and d=3 So, \(22=a_1+3{\rm (3)}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So solve for \(a_1\). (apologize for going from notation of f(n) to \(a_n\), and hope that is ok:) )

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0It's fine and is the answer 31? I'm going to add this is my notes!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(22=a_1+3(3)\) \(22=a_19\) \(31=a_1\) yes, 31 is correct.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I apologize, I had to depart (buying stuff at home depot for fuuture further bath constructions)
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