Hence, the functions that produce given sequence are:
f(n) = 2n + 1
f(n) = 2(n − 1) + 3
Further explanation:
We will put n=1,2,3,4,5 to find which functions give the given sequence
f(n) = 2n − 1
Putting values of n
[tex]f(1)=2(1)-1=2-1=1\\f(2)=2(2)-1=4-1=3\\f(3)=2(3)-1=6-1=5[/tex]
This function doesn't generate the given sequence
f(n) = 2n + 1
Putting values of n
[tex]f(1)=2(1)+1=2+1=3\\f(2)=2(2)+1=4+1=5\\f(3)=2(3)+1=6+1=7\\f(4)=2(4)+1=8+1=9\\f(5)=2(5)+1=10+1=11[/tex]
This function generates the given sequence.
f(n) = 2(n − 1) − 3
Putting values of n
[tex]f(1) = 2(1 -1) -3=2(0)-3=0-3=-3\\f(2) = 2(2 -1) -3=2(1)-3=2-3=-1\\f(3) = 2(3-1) -3=2(2)-3=4-3=1[/tex]
This function doesn't generate the given sequence
f(n) = 2(n − 1) + 3
Putting values of n
[tex]f(1) = 2(1 - 1) + 3=2(0)+3=0+3=3\\f(2) = 2(2 - 1) + 3=2(1)+3=2+3=5\\f(3) = 2(3 - 1) + 3=2(2)+3=4+3=7\\f(4) = 2(4 - 1) + 3=2(3)+3=6+3=9[/tex]
Hence, the functions that produce given sequence are:
f(n) = 2n + 1
f(n) = 2(n − 1) + 3
Keywords: Functions, Sequence
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