Find f( 1 ) , f( 2 ) , f( 3 ) , f( 4 ) , and f( 5 ) if f(n) is definedrecursively by f( 0 ) = 3 and for n = 0 , 1 , 2 a) f(n + 1 ) = − 2 f(n) . b) f(n + 1 ) = 3 f(n) + 7. c) f(n + 1 ) = f(n) 2 − 2 f(n) − 2. d) f(n + 1 ) = 3 f( slader

Answer and explanation:

To find : f(1) , f(2) , f(3) , f(4) , and f(5) if f(n) is defined recursively by f(0) = 3 and for n = 0 , 1 , 2 ,... ?

Solution :

We have given, f(0) = 3 for all parts.

a)

For f(1) put n=0,

For f(2) put n=1,

For f(3) put n=2,

For f(4) put n=3,

For f(5) put n=4,

b)

For f(1) put n=0,

For f(2) put n=1,

For f(3) put n=2,

For f(4) put n=3,

For f(5) put n=4,

c)

For f(1) put n=0,

For f(2) put n=1,

For f(3) put n=2,

For f(4) put n=3,

For f(5) put n=4,

d)

For f(1) put n=0,

For f(2) put n=1,

For f(3) put n=2,

For f(4) put n=3,

For f(5) put n=4,

-2

7 - 9 = -2

reversed:

-2 + 9 = 7

take it another