Question

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

Answer 1

ANSWER

The general term of the sequence is.

$t_n= 11 - 13(n - 1)$

The correct answer is C.

EXPLANATION
The recursive definition of the sequence is given by

$t_n=t_{n-1}-13$
where
$t_1=11$

and
$n > 1.$

When we plug in
$n = 2$
into the recursive definition, we obtain,

$t_2=t_{2-1}-13$


$\Rightarrow t_2=t_{1}-13$

$\Rightarrow \: t_2=11-13$

$t_2= - 2$

The Commons difference is
$d = - 2 - 11 = - 13$

The general term is given by the formula,

$t_n= t_1 + (n - 1)d$

We substitute the above values to obtain,

$t_n= 11 + (n - 1)( - 13)$

This implies that,

$t_n= 11 - 13(n - 1)$

where,
$n\in N$