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.