定义运算“⊙”:a⊙1=a,a⊙n=2[a⊙(n-1)]+a,(n>1) 已知m⊙4=30,则m=_,m⊙5=_.
问题描述:
定义运算“⊙”:a⊙1=a,a⊙n=2[a⊙(n-1)]+a,(n>1)
已知m⊙4=30,则m=______,m⊙5=______.
答
因为m⊙2=2[m⊙(2-1)]+m,
=2m+m=3m,
m⊙3=2[m⊙2]+m,
=2×3m+m,
=7m,
m⊙4=2[m⊙3]+m,
=2×7m+m,
=15m,
即15m=30,
所以m=2,
(2)m⊙5=2[m⊙4]+m,
2×15m+m,
=31m,
即31m=31×2=62,
故答案为:2;62.