Question

Find the second term “t2” of the recursive function described below tn= tn-1-tn-2 t8=20 t6 =13

Answer 1

The second term is, t₂ = 20.

Explanation:

The recursive function described is as follows:

`t_(n)= t_(n-1)-t_(n-2)`

Given:

`t_(8)=20\\\\t_(6)=13`

Compute the 7th term as follows:

`t_(8)= t_(7)-t_(6)\\\\t_(7)=t_(8)+t_(6)\\\\t_(7)=20+13\\\\t_(7)=33`

Compute the 5th term as follows:

`t_(7)= t_(6)-t_(5)\\\\t_(5)=t_(6)-t_(7)\\\\t_(5)=13-33\\\\t_(5)=-20`

Compute the 4th term as follows:

`t_(6)= t_(5)-t_(4)\\\\t_(4)=t_(5)-t_(6)\\\\t_(4)=-20-13\\\\t_(4)=-33`

Compute the 3rd term as follows:

`t_(5)= t_(4)-t_(3)\\\\t_(3)=t_(4)-t_(5)\\\\t_(3)=-33+20\\\\t_(3)=-13`

Compute the 2nd term as follows:

`t_(4)= t_(3)-t_(2)\\\\t_(2)=t_(3)-t_(4)\\\\t_(2)=-13+33\\\\t_(2)=20`

Thus, the second term is, t₂ = 20.