Question

g(n)=−50−15ng, left parenthesis, n, right parenthesis, equals, minus, 50, minus, 15, n Complete the recursive formula of g(n)g(n)g, left parenthesis, n, right parenthesis. g(1)=g(1)=g, left parenthesis, 1, right parenthesis, equals

Answer 1

Answer:

  g(n) = g(n-1) -15

  g(1) = -65

Step-by-step explanation:

We can find the recursive formula from the explicit formula for this arithmetic sequence by substituting 1 and (n+1) for n in the explicit formula.

__

  g(n+1) = -50 -15(n+1) = (-50 -15n) -15 . . . . . find g(n+1)

  g(n+1) = g(n) -15

and ...

  g(1) = -50 -15(1) = -65

Then the recursive formula can ge written as ...

  g(n) = g(n-1) -15

  g(1) = -65

_____

Additional comment

We found g(n+1) = g(n) -15. Substituting n-1 for n in this formula puts it in the form we need for answering the question:

  g((n-1)+1) = g(n-1) -15

  g(n) = g(n -1) -15

Either of these forms tells you how to get the next term from the previous one.