Question

Complete the recursive formula of the arithmetic sequence 20,26,32,38

Answer 1

A recursive formula for a sequence expresses the $n$-th term as a function of the previous one(s).

In this case, you can see that every term is 6 more than the previous one.

So, the recursive formula is "the $n$-th term is 6 more than the $n-1$-th term".

In formula, it's written

$a_n=a_{n-1}+6$

Since the recursion could go back indefinitely, we usually set a starting point, so that the sequence is fully determined:

$\begin{cases}a_0=20\\a_n=a_{n-1}+6\end{cases}$