Find the number of terms in this AP The AP is defined as follows:

$$
7 + 9 + ... + (2n + 1)
$$

If I remember correctly the answer given was $n-2$.

But I thought that since $n$ was defined as the number of terms in the progression, the answer should always be $n$.

How can the answer be $n - 2$ (or in fact anything other than $n$).

Thanks in advance for the help
Find out the common difference denoted by $d_1$.    

Let the first term be represented by $A$ and let the last term be represented by $L$.   

Calculate number of terms $T$ using the formula :
$T = \frac{L-A}{d_1} + 1$. We thus get $T = n-2$ using $L = 2n+1$ and $A= 7$.    



As to why the answer is $n-2$, one can explain it in terms of the direct consequence of the formula. It is not always necessary that the number of terms in a sequence should be $n$. Your sequence is that of the odd numbers starting from $7$ and not from $3$. The latter case would have given you $n$ terms. Hope it helps.
$$
1+\frac{1}{2}((2n+1)-7)=n-2.
$$