Question

Write the Recursive Rule for the sequence:

Answer 1

A formula is recursive if it expresses the term $a_n$ in terms of the previous one(s) $a_{n-1},\ a_{n-2},\ \ldots,\ a_1$

In this case, every term is 7 more than the previous one, so the formula for $a_n$ will only involve $a_{n-1}$:

$a_n = a_{n-1} + 7$

In fact, this formula is simply saying: for every index $n$, the term with that index is 7 more than the term before.

Also, we have to specify the starting point (otherwise we would go backwards indefinitely), so the complete recursive formula is

$a_n = a_{n-1} + 7,\quad a_1 = 2$

which means: start with 2 and generate every other term by adding 7 to the previous one.