The best way to solve such questions is by taking the example of strings and try for neglecting the options.
1 bit binary strings : {0,1}
2 bit binary strings :{00.01,10,11}
3-bit binary strings:{000,001,010,011,100,101,110,111}
a1=2
a2=3
a3=5
Now try to calculate a3 from the given options..
A) an =an-1 + 2an-2 a3 = a2 + 2a1 = 3 + 2*2 =7
B) an = an-1 + an-2 a3 = a2 + a1 = 3 + 2 = 5
C) an = 2an-1 + an-2 a3 = 2*a2 + a1 = 2*3 + 2 =8
D) an =2an-1 +2an-2 a3 = 2*a2 + 2*a1 =2*3 + 2*2 = 10
Only B is Correct....