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The last time Rovers did that was a run of five to start the 2024/25 campaign under John Eustace.
Victory against Wrexham would also see them equal the number of wins they managed at home in the entirety of last season (4).
“I think everyone’s looking forward to getting back to Ewood after two tough away games at Bristol City and West Brom," Carter said.
“We’re looking forward to getting back and having that home support.
“Form at home was something we struggled with last season and we found it a really difficult season, largely because of that, so it shows how important your home form is.
“I don’t know why we couldn’t get those wins at home, but the support this season has been brilliant all season and I hope we can get the same this weekend," he added. "I hope we can give the fans something to celebrate.
“Any team that does well in a season, it’s usually the home record that gets them in those top positions.
“The fans have been crucial for us and we’ll need them on Saturday and for the rest of the season; that’s for definite.”