Arithmetic Sequence!

Let $n$ be the common difference between every two consecutive terms.

Note that:

$a = c - 2n$ ,

$b = c - n$ ,

$c = c$ ,

$d = c + n$ , and

$e = c + 2n$

$\implies a+b+c+d+e = (c-2n)+(c -n ) + c + ( c + 2n ) + (c + n) = 5c = 125 \implies c = 25.$

We can not find other terms since $n$ which is the common difference is unknown.

Let the common difference of the arithmetic progression be $\delta$ . Then

$\begin{aligned} a + b + c + d + e & = 125 \\ (c-2\delta) + (c - \delta) + c + (c + \delta) + (c + 2\delta) & = 125 \\ 5c & = 125 \\ \implies c & = 25 \end{aligned}$

The value of $\boxed c$ can be found.