Question

a⊙1=a,a⊙n=2[a⊙(n-1)]+a,(n＞1),已知m⊙4=30,则m=( ),m⊙5=( )

Answer 1

m⊙4

=2[m⊙(4-1)]+m

=2(m⊙3)+m

=30

m⊙3=(30-m)/2

2[m⊙(3-1)]+m=(30-m)/2

m⊙2=[(30-m)/2-m]/2

2[m⊙(2-1)]+m=(30-3m)/4

2(m⊙1)+m=(30-3m)/4

2m+m=(30-3m)/4

12m=30-3m

m=2

m⊙5

=2[m⊙(5-1)]+m

=2(m⊙4)+m

=2×30+2

=62