Question

, list the first five terms of each sequence. f(n + 1) = −2f(n) + 8 and f(1) = 1 for n ≥ 1

Answer 1

Answer: 1, 7, 1, 7, 1.

Step-by-step explanation:

The given function :  $f(n+1)=-2f(n)+8$ and  f(1) = 1 for n ≥ 1

We put value of n=1,2,3,4 , we get

For n=1  , $f(2)=f(1+1)=-2f(1)+8=-1(1)+8=-1+8=7$

For n=2  , $f(3)=f(2+1)=-2f(2)+8=-1(7)+8=1$

For n=3  , $f(4)=f(3+1)=-2f(3)+8=-1(1)+8=7$

For n=4  , $f(5)=f(4+1)=-2f(4)+8=-1(7)+8=1$

Hence, the  first five terms of the given sequence are 1, 7, 1, 7, 1.