Question

对任意自然数a，b，规定a#b=2*a+b，若a#2a#3a#4a#5a#6a#7a#8a#9a=2026

a=

Answer 1

a#b=2*a+b
所以a#2a=2a+2a=4a
a#2a#3a=4a#3a=8a+3a=11a
a#2a#3a#4a=11a#4a=22a+4a=26a
同理
a#2a#3a#4a#5a=57a
a#2a#3a#4a#5a#6a=120a
a#2a#3a#4a#5a#6a#7a=247a
a#2a#3a#4a#5a#6a#7a#8a=502a
a#2a#3a#4a#5a#6a#7a#8a#9a=1013a
所以1013a=2026
a=2

Answer 2

a#2a#3a#4a#5a#6a#7a#8a#9a
1*2+2=4
4*2+3=11
11*2+4=26
26*2+5=57
57*2+6=120
120*2+7=247
247*2+8=502
502*2+9=1013
原式化为：
1013a=2026
a=2