Chapter 6.6, Problem 51E

To determine

To find:The 2^nd, 5^th, and 10^th terms of the sequence.

Answer to Problem 51E

The required terms are $f(2)=15,f(5)=-15,f(10)=-10$ .

Explanation of Solution

Giveninformation:

The function $f$ represents a sequence.

  $f(1)=10,f(2)=15,f(n)=f(n-1)-f(n-2)$

It is already given that the 2^nd term of the sequence is $f(2)=15$ .

Using $f(n)$ :

  $\begin{array}{l}f(3)=f(3-1)-f(3-2)=f(2)-f(1)=15-10=5\\ f(4)=f(3)-f(2)=5-15=-10\\ f(5)=f(4)-f(3)=-10-5=-15\\ f(6)=f(5)-f(4)=-15-(-10)=-5\\ f(7)=f(6)-f(5)=-5-(-15)=10\\ f(8)=f(7)-f(6)=10-(-5)=15\\ f(9)=f(8)-f(7)=15-10=5\\ f(10)=f(9)-f(8)=5-15=-10\end{array}$

Conclusion:

Therefore, the required terms are $f(2)=15,f(5)=-15,f(10)=-10$ .