What is the $87^{\mathrm{th}}$ odd positive integer?
I want to find the $87^{\mathrm{th}}$ odd positive integer, so I need to come up with a way to relate the position of an odd number in the sequence of all odd numbers to the value of that odd number. One way to do this is to notice that the $n^{\mathrm{th}}$ odd number is always $2n - 1$. For example, the first odd number is $2 \cdot 1 - 1 = 1$, the second odd number is $2 \cdot 2 - 1 = 3$, and so on. So, to find the $87^{\mathrm{th}}$ odd number, I just need to plug in $n = 87$ into the formula $2n - 1$. Doing that, I get $2 \cdot 87 - 1 = 174 - 1 = 173$. Therefore, the $87^{\mathrm{th}}$ odd positive integer is 173. 