Question 164033

(Please show source)
.................n
ABBA.............1     2 Bs    2 As
AABBBAA..........2     3 Bs    4 As
AAABBBBAAA.......3     4 Bs    6 As
AAAABBBBBAAAA....4     5 Bs    8 As
........

AAA,,,BBB,,,,AAA.n    n+1 Bs   2n As

Answer: Number of Bs in the nth term is n+1

we have to find n such that 
 Bs/Total =0.35
then

(n+1)/(n+1+2n)=0.35
n+1=0.35(3n+1)

n-(1.05)n=0.35-1
-0.05n=-0.65
n=0.65/0.05=13

Answer: n=13