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episode 3 "Acafellas"
The 1st. Pilot
I FOUND IT! I too have been looking for it. Its Season 6 Episode: Sing, Sing, Sing!
on episode 85
Episode 3: Looking for Lucky
The Glee Episode In Which Finn Happens To Sing Jesse's Girl To Rachel Is Laryngitis
In the episode named "Britney/Brittany"!
Season 2 episode 1 I think
I read this question while I happened to be listening to her sing firework. But Rachel is the main person on Glee and she has the strongest voice for singing and sometimes, not always she does sing better then everyone else that plays a teenager on Glee. But it is mostly because she is the main person.
Hell-o (Season 1, episode 14)
Episode 2 - Britney/Brittany
Rachel sings ...Baby One More Time in Glee's Britney Spears tribute episode, Britney/Brittany (Season 2, episode 2).
Born This Way. S2 Ep18.
She sings Firework in season 2 episode 12. ;)
She sings this song in season 1- episode 13 Hell-O to Jesse when he breaks up with her.
It was featured in Pilot and Hairography, both by Finn and Rachel.