c 1=a，q=( 1+5)%= 1.05
General term: cn = a *1.05 (n-1)1≤ n ≤12, and it is an integer.
= a n > 12 and is an integer.
Sum of the first n terms: bn = c1(1-q n)/(1-q) = 20a (1.05n-1)1≤ n ≤/kloc-.
= b12+(n-12) a = (n+4) a n >12 and is an integer.
{an} is also a constant sequence starting from the thirteenth item.
an = 10a+(n- 1)a-b(n- 1)
= (n+9) a-20a (1.05n-1)1≤ n ≤12, and it is an integer.
= (n+9) a-(n+4) a = 5an > 12, and it is an integer.
(2) The winning rate yn=cn/an × 100%, the molecule cn rises first and then remains unchanged, and the denominator an falls first and then remains unchanged.
Yn rises first and then remains unchanged, and the maximum value is y12 = c12/a12×100%.
=a* 1.05^( 12- 1)/5a× 100%
= 1.7/5× 100%
=34%
The highest winning rate of 20 12 and 12 is 34%.