I recently made an Sorcerer/Eldritch Knight that has the Arcane Bloodline.
I was looking at how a character would gain spells known from the prestige class. The entry reads thus:
"At the indicated levels, an Eldritch Knight gains new spells per day as if he had also gained a level in an arcane spellcasting class he belonged to before adding the prestige class. He does not, however, gain any other benefit a character of that class would have gained, except for additional spells per day, spells known (if he is a spontaneous spellcaster), and an increased effective level of spellcasting."
Normally, when advancing the spellcasting of a spontaneous-casting EK (or Arcane Archer or other PrC that advances spellcasting), this is interpreted to mean that the character receives the bonus spells granted from their bloodline--but they would not receive any bloodline powers. Here's what I'm getting at: One of the boons granted from the Arcane Bloodline is "Extra Arcana", which grants additional spells at specific levels. Based on how an Eldritch Knight gains spells known, these "Extra Arcana" spells should be gained in addition to the spells granted from the base bloodline. In other words, a hypothetical Sorcerer 1/Fighter 1/Eldritch Knight 10/Arcane Archer 8 (we gained early entry into EK by virtue of being an Aasimar), with the Arcane bloodline would learn an additional spell at levels 11 and 16.
Does this seem accurate? I'm relatively new to Pathfinder, but I've done my homework, and I think that RAW supports this interpretation. It's something I've never seen mentioned on any forums or in any guides, and if I'm correct, it's a nice bonus for multiclassed Sorcerers who select the Arcane bloodline.