Question

estion 2
A sequence is dened recursively as:
f(0)=-1;f(1)=1;
f(n)=f(n-1) - f(n-2)
What will be thw value of f(6)?
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Answer 1

Given:

• $f(0)=-1,\:f(1)=1,\\f(n)=f(n-1)-f(n-2)$

To find: the value of $f(6)$

Solution:

• Given $f(n)=f(n-1)-f(n-2)$

• When $n=2$, we get

• $f(2)=f(1)-f(0)=1-(-1)\\=1+1=2$

• When $n=3$, we get

• $f(3)=f(2)-f(1)=2-1=1$

• When $n=4$, we get

• $f(4)=f(3)-f(2)=1-2=-1$

• When $n=5$, we get

• $f(5)=f(4)-f(3)=-1-1=-2$

• When $n=6$, we get

• $f(6)=f(5)-f(4)=-2-(-1)\\=-2+1=-1$

Answer: $f(6)=-1$

Remark:

• To solve this type of problems, first write down the given nth term.

• Then to find n = m, find the previous terms by putting k = 0, 1, 2, 3, ..., m - 1 and then you will find n = m.