Question

The explicit rule for a sequence is

an=17−5n .

What is the recursive rule for the sequence?

can you explain also

Answer 1

The general form of an explicit rule for an arithmetic sequence is
$a_n=a_1+d(n-1)$, where a₁ is the first term of the sequence and d is the common difference.  Since we have $a_n=17-5n$, we know that n is multiplied by 5.  That means that d must be 5, since that is the only thing that n gets multiplied in our general form.  This gives us:
$a_n=a_1+5(n-1) \\ \\a_n=a_1+5*n-5*1 \\ \\a_n=a_1+5n-5$
We know that we add something to 5n and then subtract 5 to get 17.  Cancelling this process, we can add 5 to 17 to get 22.  This gives us
$a_n=22+5(n-1)$
We know that our first term, a₁, is 22 and our common difference, d, is 5.
The general form of a recursive formula for an arithmetic sequence is 
$a_n=a_n_-_1+d$, where d is the common difference and $a_n_-_1$ is the previous term.  We know that d is 5, so our recursive formula is
$a_n=a_n_-_1+5$

Answer 2

Answer:

$a_{n} = a_{n-1}-5$

$a_{1} = 12$

Step-by-step explanation: