Question

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

Answer 1

Solution :

-> F ( n + 1 ) = F ( n ) - 3

=> F ( n ) = F ( n - 1 ) - 3 
=> F ( n + 1 ) + ... F ( 2 ) = F ( n ) + F ( n - 1 ) + ... + F ( 1 ) - 3( n )
=> F ( n + 1 ) = F ( 1 ) - 3n

Hence => F ( 4 ) = F( 1 ) - 3( 3 )
           => 22 + 9 = F ( 1 )
           => F( 1 ) = 31

____________________________________________________________

                                               OR

F ( 4 ) = F ( 3 + 1 ) = F ( 3 ) - 3 = F ( 2 + 1 ) - 3 
                              = F ( 2 ) - 3 - 3 
                              = F ( 1 ) - 3 - 3 - 3
=> F ( 4 ) = F ( 1 ) - 9
=> F ( 1 ) = 22 + 9 = 31 √√