For sequences with the same positive first term a, which statement correctly compares the nth terms of an arithmetic progression (common difference d>0) and a geometric progression (common ratio r>1) as n increases?
a) The nth term of the AP eventually exceeds that of the GP because the constant difference d accumulates faster than a small ratio r.
b) The nth term of the GP grows exponentially faster than that of the AP.
c) Both the AP and GP grow at the same overall rate when r is close to 1, so neither ultimately dominates.
d) The GP overtakes the AP only if r>da; otherwise the AP stays larger for all n."