Question

Consider the recursively defined function below. f(1)=-5.25 f(n)=f(n-1)+1.75, for n=2,3,4,.... Create the first five terms of the sequence defined by the given function. Tiles: [-7.5], [-1.5], [-1.75], [-5.25], [1.75], [-3.5], [0], [1.5] Sequence: ?

Answer 1

N=1→f(n)=f(1)=-5.25 (First term)
f(n)=f(n-1)+1.75, for n=2, 3, 4, ...

Second term:
n=2→f(2)=f(2-1)+1.75=f(1)+1.75=-5.25+1.75→f(2)=-3.5

Third term:
n=3→f(3)=f(3-1)+1.75=f(2)+1.75=-3.5+1.75→f(3)=-1.75

Fourth term:
n=4→f(4)=f(4-1)+1.75=f(3)+1.75=-1.75+1.75→f(4)=0

Fifth term:
n=5→f(5)=f(5-1)+1.75=f(4)+1.75=0+1.75→f(5)=1.75

Answer:
Sequence of the terms:
First, second, third, fourth, fifth:
-5.25, -3.5, -1.75, 0, 1.75