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Select ALL the correct answers.Consider the arithmetic sequence below.-5, 4, 13, 22, 31, ...Select all functions that define the given sequence.Of(1) = -5, f(n) = -f(n - 1) + 9, for n 2 2f(1) = -5, f(n) = f(n - 1) + 9, for n z 2Of(1) = -5, f(n) = f(n-1) + 7, for n 2 2fin) = -5n + 9O fin) = 9n - 5fin) = 9n - 14

Select ALL the correct answersConsider the arithmetic sequence below5 4 13 22 31 Select all functions that define the given sequenceOf1 5 fn fn 1 9 for n 2 2f1 class=

Respuesta :

From the given sequence ,we can note that the common difference between consecutive numbers is 9. Thats because

[tex]\begin{gathered} 4-(-5)=9 \\ 13-4=9 \\ 22-13=9 \\ 31-22=9 \end{gathered}[/tex]

This means that

[tex]f(n)-f(n-1)=9[/tex]

or equivalently,

[tex]f(n)=f(n-1)+9\text{ for n}\ge2[/tex]

We can also obtain the same result by taking into account the common difference and the fact that the first number in the sequence is -5. So we can write

[tex]f(n)=9n-5[/tex]

For instance,

[tex]\begin{gathered} n=0\Rightarrow f(0)=-5 \\ n=1\Rightarrow f(1)=9-5=4 \\ n=2\Rightarrow f(2)=18-5=13 \\ n=3=f(3)=27-5=22 \\ n=4\Rightarrow f(4)=36-5=31 \end{gathered}[/tex]

Therefore, the functions that define the given sequence are:

[tex]\begin{gathered} f(1)=-5,\text{ f\lparen n\rparen=f\lparen n-1\rparen+9 for n}\ge2 \\ and \\ f(n)=9n-5 \end{gathered}[/tex]

which correspond to options 2 and 5 from top to bottom.

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