The explicit rule for a sequence is given. an=−2n+7 what is the recursive rule for the sequence? a1=7;  an=an−1+2 a1=5;  an=an−1−2 a1=−2;  an=an−1+7 a1=7;  an=an−1−2

As is often the case with multiple-choice questions, you can choose the correct answer by seeing if they are consistent with the problem statement.

an = -2n +7
means that the value of a1 can be found from
a1 = -2*1 +7
a1 = 5

Only one of the choices matches this condition: the correct one.

The 2nd selection is appropriate.


If you want to actually work the problem, you find a[1] as above. Then, consider
.. a[n+1] = -2*(n+1) +7
.. = (-2n +7) -2 . . . . . . note the stuff in parentheses matches the definition of a[n]
.. = a[n] -2
This is also true for the previous pair of terms:
.. a[n] = a[n -1] -2

So, now you have
.. a[1] = 5
.. a[n] = a[n-1] -2
which matches the second selection.