The terms of the sequence are 5, -1, -7
Let us find the common difference between each two consecutive terms
-1 - 5 = -6
-7 - (-1) = -7 + 1 = -6
Then the common difference is -6
The first term is 5
The recursive formula is
[tex]a_1=1stterm;a_n=a_{n-1}+d[/tex]Substitute in the formula the value of the 1st term and d the common difference
[tex]a_1=5;a_n=a_{n-1}+(-6)[/tex]Remember (+)(-) = (-)
[tex]a_1=5;a_n=a_{n-1}-6[/tex]This is the recursive formula for the sequence
