I have the answer to this but I'm not sure that I entirely understand it.

Find the number of terms in the AP: 7 + 9 +...+ (2n+1)

My solution:

The ath term will be 2a + 5 so 2a + 5 = 2n + 1 therefore a = n - 2

This gives me the right answer but what I don't understand is what the difference between n and a is? Initially I thought that they were the same value but of course that is not possible. I would normally think of the 'ath term' as the 'nth term' so is (2n+1) just an expression that happens to use n as a variable just to be awkward?

I would really appreciate it if somebody could clarify this for me.

Merry Christmas!