Question: Puyo Puyo Fever 2, is a video game developed by Sonic Team and published by Sega, it was released as a sequel to the previous title, "Puyo Pop Fever", a puzzle video game, and is which number main installment in the "Puyo Puyo" puzzle game series?

Context articles: Puyo Puyo (video game)
Puyo Puyo Fever 2
Puyo Puyo Tetris
Puyo Puyo!! 20th Anniversary
Puyo Puyo~n
Puyo Puyo
Puyo Puyo! 15th Anniversary
Puyo Pop Fever
Puyo Puyo BOX
Puyo Pop (video game)

Puyo Puyo (ぷよぷよ , Puyo Puyo ) is a puzzle video game released in 1991 by Compile for the MSX2.
 Since its creation, it uses characters from "Madou Monogatari".
 It was created by Masamitsu "Moo" Niitani, the founder of Compile, who was inspired by certain elements from the "Tetris" and "Dr. Mario" series of games.
Puyo Puyo Fever 2 (ぷよぷよフィーバーチュー!
 , Puyopuyo Fībā Chū! )
 is a video game developed by Sonic Team and published by Sega.
 The game was released as a sequel to the previous title, "Puyo Pop Fever".
 The gameplay remains relatively unchanged, but several new modes are introduced.
 The game features nine different plots, each one pertaining to its three protagonists.
 "Puyo Puyo Fever 2" was released exclusively in Japan for the PlayStation 2 and PlayStation Portable in November 2005, and later for the Nintendo DS the following month.
Puyo Puyo Tetris (ぷよぷよテトリス , Puyopuyo Tetorisu ) is a puzzle video game developed by Sonic Team and published by Sega.
 The game is a crossover between the "Puyo Puyo" series and the "Tetris" franchise, and features various gameplay modes incorporating both aspects.
 The game includes characters modeled after the seven Tetrominos, which are different puzzle pieces each made of four blocks.
Puyo Puyo!!
 20th Anniversary is a puzzle game developed by Sonic Team and published by Sega.
 The game honored the twentieth year of the "Puyo Puyo" series, and was first released for the Nintendo DS in July 2011, and later for Wii, Nintendo 3DS, and PlayStation Portable in December 2011.
Puyo Puyo~n (ぷよぷよ〜ん , Puyopuyōn ) , also known as Puyo Puyo 4, and Puyo Puyo~n Party (for the N64 version) is the fourth installment of the Puyo Puyo puzzle game series, created by Sega and Compile for the Sega Dreamcast, Sony PlayStation, Nintendo 64 and Game Boy Color.
 Like many of the Puyo Puyo games, it was never officially released outside Japan.
 The title of "Puyo Puyo~n" comes from the Japanese word "yon" (四 , meaning four) , signifying the fourth game in the series.
 Plans were made for a 64DD version entitled Puyo Puyo~n 64 (ぷよぷよ〜ん , Puyopuyōn rokujuon ) , but it was later cancelled.
Puyo Puyo (ぷよぷよ), previously marketed under the name Puyo Pop in North America and Europe, is a series of tile-matching video games created by Compile.
 Sega has owned the franchise since 1998, with most releases after 2001 being developed by Sonic Team.
 Puyo Puyo was created as a spin off franchise to "Madou Monogatari" ("Story of Sorcery"), a series of first-person dungeon crawler RPGs by Compile.
 The characters from "Puyo Puyo" originated from "Madou Monogatari".
 As of 2016, Sega Sammy Holdings has reported that the "Puyo Puyo" franchise has sold a combined total of 22 million units in physical and digital sales since Sega obtained the rights.
Puyo Puyo!
 15th Anniversary (ぷよぷよ!
 , Puyopuyo! )
 is a sub-story of the Puyo Puyo series, developed by Sonic Team and published by Sega for the Nintendo DS, PlayStation 2, PlayStation Portable, and Wii.
 As with many other games in the series, it has not been released outside Japan for any consoles.
 This is the first Puyo Puyo game to be released on the Wii console.
 The game was endorsed by Yuri Ebihara.
Puyo Pop Fever (ぷよぷよフィーバー (Puyopuyo Fībā ) , is a puzzle video game developed by Sonic Team.
 It is the fifth main installment in the "Puyo Puyo" puzzle game series and the second "Puyo Puyo" game to be programmed by Sonic Team after "Puyo Pop" (which was released just after the series' original developer, Compile, went bankrupt).
 Sega, which acquired the series' rights from Compile in 1998, published all the Japanese versions of the game; the game was scarcely released internationally, and certain versions were released by other publishers in those areas.
 Only the Nintendo GameCube and DS versions were released in North America; Europe received both versions plus the Xbox, PlayStation 2, Game Boy Advance, and PlayStation Portable versions.
 The NAOMI port to Dreamcast, released only in Japan, was the last Dreamcast game developed by Sonic Team, as well as being the only console version to use sprites in place of 3D models.
Puyo Puyo BOX is a compilation video game developed by Compile for the Sony PlayStation.
 It is Compile's last recognised "Puyo Puyo" title in the series before Sega, previously only owning the character rights, fully obtained the rights to the series.
 "Puyo Puyo BOX", being a compilation, primarily consists of earlier "Puyo Puyo" games, but also contains original content.
Puyo Pop, known as Minna de Puyo Puyo (みんなでぷよぷよ , "Everybody Puyo Puyo") in Japan, is the first of the Puyo Puyo games made for the Game Boy Advance, and the first produced by Sonic Team after Compile went bankrupt and sold the rights to Sega.
 However, at the same time, it is the last to use the original Madou Monogatari cast.
 It was not counted in the "official" sequence, nor were the later "Anniversary" games, as evidenced by the naming of Puyo Puyo 7.