Given the arithmetic sequence 7,5,3,1,-1,
write the recursive rule.

Given the arithmetic sequence 7, 5, 3, 1, -1 Then the recursive rule is

Solution:

Given that, an arithmetic sequence is 7, 5, 3, 1, - 1  

We have to write the recursive rule for the above given arithmetic sequence

Now, let us find the common difference for the above given arithmetic sequence,

Common difference d = any term of sequence – its previous term

d = 5 – 7 = - 2

So, common difference d = - 2

Now, we know that, recursive rule is an equation that gives the next value by performing certain operation on the previous value.

Here for any arithmetic sequence, it will be nth term = (n – 1)th term + common difference

Hence, the recursive rule is