A particle travels in a region containing a uniform magnetic field...

Let the uniform electric and magnetic fields be directed along the z-axis, so $\vec{E} = E \hat{k}$ and $\vec{B} = B \hat{k}$.

The initial velocity of the particle is perpendicular to the fields. Let $\vec{v} = v_0 \hat{i}$.

The magnetic force acting on the particle is $\vec{F}_m = q(\vec{v} \times \vec{B})$, which provides the necessary centripetal force to move the particle in a circular path in the plane perpendicular to the magnetic field. The radius of this circular path is constant since the perpendicular speed remains constant.

The electric force acting on the particle is $\vec{F}_e = q\vec{E}$, which provides a constant acceleration $a = \dfrac{qE}{m}$ along the direction of the fields.

Due to this acceleration, the component of velocity parallel to the fields increases continuously with time ($v_{\parallel} = at$).

The combination of uniform circular motion in the perpendicular plane and accelerated motion along the parallel direction results in a helical path.

The pitch of the helix is the distance traveled along the magnetic field during one complete revolution. Since the velocity along the field is increasing, the pitch increases with time. Thus, the path is a helix with nonuniform pitch.