Complete the recursive formula of the arithmetic sequence - 1, - 13, - 25, - 37

The recursive formula is aₙ=aₙ₋₁ - 12

Step-by-step explanation:

Recursion is a process in which each step of a pattern depends on the step or the previous steps. So a recursive sequence is a sequence where terms are defined using one or more previous terms that are given.

So a recursive formula allows you to find any term in an arithmetic sequence using a function of the previous term, where each term is the sum of the previous term and the common difference.

So, in this case you can see the common difference of all the terms by doing the following calculations between a term and its previous value:

-13 - (-1) = -13+1=-12

-25 - (-13) = -25+13=-12

-37 - (-25) = -37+25=-12

The common difference is - 12

So, the recursive formula is aₙ=aₙ₋₁ - 12 where each term is the same to the previous term minus 12.