There is a reason both times and seasons are used in this passage. Times refers to time in its duration, whether a longer or shorter period. Seasons draws attention to the characteristics of the period. The first deals with the measurement of time, the second with the suitable or critical nature of the time.
Bother terms are plural. Times refers to the ages which may pass before the Rapture occurs. Seasons has more to do with the events which will take place during these times. Other translations refer to times and epochs, or times and dates.
It is amazing to me that there is such a wealth of meaning in two little words. So many scriptures come to mind; II Tim 3:16 and Proverbs 30:5 are right at the top of my memory, teaching us that every word God inspired the writers to use is significant. There are no wasted words, no rabbit trails, in scripture. It is all profitable, and there is something we can learn from every detail.