Answer:
The second term is, t₂ = 20.
Step-by-step explanation:
The recursive function described is as follows:
[tex]t_{n}= t_{n-1}-t_{n-2}[/tex]
Given:
[tex]t_{8}=20\\\\t_{6}=13[/tex]
Compute the 7th term as follows:
[tex]t_{8}= t_{7}-t_{6}\\\\t_{7}=t_{8}+t_{6}\\\\t_{7}=20+13\\\\t_{7}=33[/tex]
Compute the 5th term as follows:
[tex]t_{7}= t_{6}-t_{5}\\\\t_{5}=t_{6}-t_{7}\\\\t_{5}=13-33\\\\t_{5}=-20[/tex]
Compute the 4th term as follows:
[tex]t_{6}= t_{5}-t_{4}\\\\t_{4}=t_{5}-t_{6}\\\\t_{4}=-20-13\\\\t_{4}=-33[/tex]
Compute the 3rd term as follows:
[tex]t_{5}= t_{4}-t_{3}\\\\t_{3}=t_{4}-t_{5}\\\\t_{3}=-33+20\\\\t_{3}=-13[/tex]
Compute the 2nd term as follows:
[tex]t_{4}= t_{3}-t_{2}\\\\t_{2}=t_{3}-t_{4}\\\\t_{2}=-13+33\\\\t_{2}=20[/tex]
Thus, the second term is, t₂ = 20.
