AMC8 2015 Problem 18

An arithmetic sequence is a sequence in which each term after the first is obtained by adding a constant to the previous term. For example, 2, 5, 8, 11, 14 is an arithmetic sequence with five terms, in which the first term is 2 and the constant added is 3 . Each row and each column in this 5 \times 5 array is an arithmetic sequence with five terms. What is the value of X ?

\begin{array}{|l|l|l|l|l|} \hline 1 & \quad & & \quad & 25 \\ \hline & & & & \\ \hline & & X & & \\ \hline & & & & \\ \hline 17 & & & & 81 \\ \hline \end{array}

Answer Choices
A. 21
B. 31
C. 36
D. 40
E. 42