The price is actually $5 for eight lessons. However the lessons started on January 10 so if you go on January 24, you will only get seven lessons for your $5.
Even at $5 for one lesson, you would get your moneys worth, so don't worry about starting at the beginning of the eight lesson group.
If you do not belong to the County Senior group, you might have to pay $10 per week until you have paid the $49 Fairfax County charges to join. This is per year, and it gives you access for one full year to all of the county's Senior activities. (They have a lot of programs and trips.)
I have been given different prices, every time I talk to anyone at the county. My understanding, from the last time I actually talked to someone from Fairfax County, is that people get at least one free visit, but that is now in question, so please assume that you will have to pay $10 per week if you haven't joined the Senior Program.