Refer to the graph of the sequence $\{c_n\}.($a$)$ Estimate the first four terms of the sequence. $($b$)$ Write a formula for the $nth$ term of the sequence. $($c$)$ Find the $40$ th term. $($d$)$ Find the sum of the first $40$ terms. $($e$)$ If $c_n=-1278,$ what is $n?($f$)$ Find the difference between $c_{75}$ and $c_{32}.$