Here's a demonstration showing just that part of the cycles particle info being used to drive a colour ramp. Notice I had to also add in another divide just to get the far end of the colour ramp to appear in the view. You can see clearly that the individual particle blurred paths are constant in colour even though different particles may have different colours. You might be able to use a spherical gradient in addition to the age and lifetime values to change colour along a long thin particle to create the effect you are looking for.

Here's a demonstration showing just that part of the cycles particle info being used to drive a colour ramp. Notice I had to also add in another divide just to get the far end of the colour ramp to appear in the view. You can see clearly that the individual particle blurred paths are constant in colour even though different particles may have different colours. You might be able to use a spherical gradient in addition to the age and lifetime values to change colour along a long thin particle to create the effect you are looking for.

Here's a crude version of the suggestion above.