Some study pirke Avos weekly through the summer, from Pesach to Rosh Hashana. Others do so only for the six Shabasos between Pesach and Shavuos, one chapter a week. I've heard the latter custom explained as providing moral preparation for Shavuos, though I don't know a source for this offhand.
In Israel, in some years, there are seven Shabasos between Pesach and Shavuos. (This occurs when the first day of Pesach is Shabas.) My question is about those who normally study pirke Avos only until Shavuos: what do they do in those years? Study chapter 1 the seventh week? Start the second week (studying nothing the first)? Something else? And why?
A source would be appreciated (especially for the "why").