Question

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

Answer 1

9514 1404 393

Answer:

  C.  31

Step-by-step explanation:

The recursive definition tells us the 4th term is 22 and the common difference is -3. This lets us write an explicit formula for the n-th term:

  f(n) = f(4) +d(n -4)

  f(n) = 22 -3(n -4) = 34 -3n

Substituting n=1 into this formula, we get ...

  f(1) = 34 -3(1) = 31

The first term is f(1) = 31.