To answer this question, we can proceed as follows:
1. We have that the recursive formula is:
[tex]T_n=T_{n-1}+T_{n-2}[/tex]
2. We have that the first term and the second term are, respectively:
[tex]T_1=3,T_2=5[/tex]
The third term
Then, to find the third term, we have:
[tex]T_3=T_{3-1}+T_{3-2}\Rightarrow T_3=T_2+T_1[/tex]
Now, we have that T1 = 3, and T2 = 5. Therefore:
[tex]T_3=T_1+T_2\Rightarrow T_3=3+5\Rightarrow T_3=8[/tex]
Now, we have that: T1 = 3, T2 = 5, T3 = 8.
The fourth term
To find the fourth term, we have:
[tex]T_4=T_{4-1}+T_{4-2}\Rightarrow T_4=T_3+T_2[/tex]
Then
[tex]T_4=T_3+T_2=8+5\Rightarrow T_4=13[/tex]
Now, we have that T1 = 3, T2 = 5, T3 = 8, T4 = 13.
The fifth term
To find the fifth term, we also have:
[tex]T_5=T_{5-1}+T_{5-2}\Rightarrow T_5=T_4+T_3[/tex]
Therefore:
[tex]T_5=13+8\Rightarrow T_5=21[/tex]
In summary, therefore, we have that the 5th term of the sequence is 21 (first option).
