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?

Answer 1

coolio

$t_1=11$

$t_n=t_{n-1}-13$

so each term is ound by subtracting 13 from the previous term

an aritmetic sequence can be written as

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

$t_n$ is the nth term

$t_1$ is the first term

d is common difference, which can also be found by doing $t_n-t_{n-1}=d$

n=wich term

we know that $t_1=11$ and we can find d

$t_n=t_{n-1}-13$, $t_n-t_{n-1}=-13=d$

so te general term is $t_n=11-13(n-1)$ which can also be expanded and written as $t_n=-13n+24$