Which term of the A.P. $3,8,13,18\dots$ is $78$?

Given A.P.: $3,8,13,18\dots$
* First term ($a$) = $3$
* Common difference ($d$) = $8-3=5$
* $n^{\text{th}}$ term ($a_n$) = $78$

The formula for the $n^{\text{th}}$ term is:

$$a_n=a+(n-1)d$$

$$78=3+(n-1)5$$

$$78-3=5(n-1)$$

$$75=5(n-1)$$

$$n-1=\frac{75}{5}=15$$

$$n=15+1=16$$

Thus, $78$ is the $16^{\text{th}}$ term.