Question

What are the first four solutions to the sequence: f(1) = 3 and f(n) = f(n-1)-5

Answer 1

Since f(1) = 3 is given we will find solutions for n = 2, 3, 4, 5

f(2) = f( 2 - 1 ) -5
= f(1) -5
We have f(1) given to us which is f(1) = 3 so we can replace f(1) with 3
= 3 - 5
= -2
f(2) = -2

f(3) = f( 3 - 1 ) -5
= f(2) -5
replace f(2) with -2 because previously we got f(2) = -2
= -2 -5
= -7
f(3) = -7

f(4) = f( 4 - 1 ) -5
= f(3) -5
replace f(3) with -7 because previously we got f(3) =-7
= -7 -5
= -12
f(4) = -12

f(5) = f( 5 - 1 ) -5
= f(4) -5
replace f(4) with -12 because previously we got f(4) = -12
= -12 -5
= -17
f(5) = -17

etc...

Therefore,

f(1) = 3
f(2) = -2
f(3) = -7
f(4) = -12
f(5) = -17
etc...

Answer 2

Solutions to selected problems from homework 1(1) The Fibonacci sequence is the sequence of numbersF(0); F(1); : : :de ned by the following recurrence relations:F(0) = 1; F(1) = 1,F(n) =F(n