An increasing sequence is formed so that the difference between consecutive terms is a constant. If the first four terms of this sequence are $x, y, 3 x+y$, and $x+2 y+2$, then the value of $y-x$ is
(A) 2
(B) 3
(C) 4
(D) 5
(E) 6
Since the difference between consecutive terms is constant, then the difference between the third and fourth terms is equal to the difference between the first and second terms, or

$$
\begin{aligned}
(x+2 y+2)-(3 x+y) & =y-x \\
y-2 x+2 & =y-x \\
2 & =x
\end{aligned}
$$

Thus, we can rewrite the sequence as $2, y, y+6$, and $2 y+4$.

Again, since the difference is constant and the difference between the second and third terms is 6 , then the difference between the first and second terms is 6 , ie. $y=8$.

Thus, $y-x=6$.

Answer: (E)

#