if f(1) =7 and f(n)=(n-1)-1 then find the value of f(5)

Answer 1

Did you make a typo (note: I often do, so I recognize them, too)?

if f(1) =7 and f(n)=(n-1)-1 then find the value of f(5)

This means that f(5) = (5-1)-1 = 4-1 = 3 [That's no fun!]

Now,

f(1) = 5

f(n) = f(n-1) - 1 for n>1

is the way to write a series in Recursive Form

The value of f(5) = f(5-1)-1 which is f(4) - 1

Now replace f(4) with f(4-1)-1 = f(3)-1 to get f(5) = ( f(3)-1) - 1 )

Now replace f(3) with f(3-1)-1=f(2)-1 . . .

. . .

f(5) = ( ( ( ( f(1) -1 ) - 1) -1 ) - 1 ) )

And the first term, f(1) = 7, so

f(5) = ( ( ( ( 7 - 1 ) - 1 ) -1 ) -1 ) )

f(5) = ( ( ( 6 -1) -1) -1) )

f(5) = ( ( 5 - 1) -1) )

f(5) = ( ( 4 - 1) )

f(5) = 3

With this recursive formula, you may also calculate terms as they occur in the series:

f(1) = 7

f(2) = 6

f(3) = 5

f(4) = 4

f(5) = 3

This is a good cross-check of your answer.