Question

A recursive rule for an arithmetic sequence is

Answer 1

From the recursive rule, you have

$a_2=a_1+7$

$a_3=a_2+7=a_1+7(2)$

$a_4=a_3+7=a_1+7(3)$

$a_5=a_4+7=a_1+7(4)$

and so on. The general pattern for the $n$-th term is adding $n-1$ copies of 7 to $a_1$:

$a_n=a_1+7(n-1)$

With $a_1=-3$, the sequence is explicitly given by

$a_n=-3+7(n-1)=7n-10$