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An arithmetic sequence is defined by the recursive formula t1 = 11, tn = tn - 1 - 13, where n ∈N and n > 1. Which of these is the general term of the sequence? A) tn = 11 - 13(n - 1), where n ∈N and n > 1 B) tn = 11 - 13(n - 2), where n ∈N and n ≥ 1 C) tn = 11 - 13(n - 1), where n ∈N and n ≥ 1 D) tn = 11 - 13(n + 1), where n ∈N and n ≥ 1

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ANSWER

The general term of the sequence is.

[tex]t_n= 11 - 13(n - 1)[/tex]

The correct answer is C.

EXPLANATION
The recursive definition of the sequence is given by

[tex]t_n=t_{n-1}-13[/tex]
where
[tex]t_1=11[/tex]

and
[tex]n > 1.[/tex]

When we plug in
[tex]n = 2[/tex]
into the recursive definition, we obtain,

[tex]t_2=t_{2-1}-13[/tex]


[tex]\Rightarrow t_2=t_{1}-13[/tex]

[tex]\Rightarrow \: t_2=11-13[/tex]

[tex]t_2= - 2[/tex]

The Commons difference is
[tex]d = - 2 - 11 = - 13[/tex]

The general term is given by the formula,

[tex]t_n= t_1 + (n - 1)d[/tex]

We substitute the above values to obtain,

[tex]t_n= 11 + (n - 1)( - 13)[/tex]

This implies that,

[tex]t_n= 11 - 13(n - 1)[/tex]

where,
[tex]n\in N[/tex]

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