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Making the transition from teen idoldom to adult pop stardom is rarely easy, but Joe, Kevin, and Nick Jonas—collectively known as Jonas Brothers—have pulled it off better than most. From their first single, the sweet and speedy pop-punk “Mandy,” through their recent album, the chart-topping “Happiness Begins,” the trio has consistently released catchy, trend-anticipating tunes, a talent that’s helped them ride the fickle world of pop tastes.

Saturday night’s show at TD Garden, their first in Boston since 2013, was a muscular run-through of the trio’s past 15 years — a chronological feat that’s even more impressive given that youngest brother Nick Jonas was only 13 when “Mandy” came out at the end of 2005. “Happiness Begins” is the band’s first proper album since 2009’s wide-ranging “Lines, Vines, and Trying Times”; the band had a bumpy ride through the 2010s as a unit, going on hiatus in 2011 and splitting after a brief reunion in 2013, although Nick found success with his R&B-tinged solo material, Kevin starred in a reality show and went the entrepreneur route, and Joe’s project DNCE hit big with the nonsensical yet deliriously fun pop-funk gem “Cake by the Ocean.”

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Despite the high tensions on display in the band’s recent documentary, “Chasing Happiness,” their comeback was an inevitability in a sense; blood is thicker than water, and it can often wash away “creative differences,” too. But they’ve made the most of it. “Happiness Begins” doesn’t rehash past glories, instead charting a course through the often-unpredictable world of streaming-era popular music. But that was even one of the band’s strengths when it was a Disney Channel darling; a medley of older hits, like the sinuous 2009 track “Paranoid” and the spiky “World War III,” worked not only because it stoked the audience’s collective nostalgia, but because of the songwriting savvy they displayed even as teenagers.

And as Saturday’s show proved, their catalog (which, Joe noted during a break, consists of 230 songs) is as varied as it is hooky. No matter their mode — storming anthems (the show opener “Rollercoaster”), bubbly reggae-pop (the muscular “Only Human”), strummed balladry (”Hesitate”), or taut rock (”Burnin’ Up”) — the Jonas Brothers stuff their songs with instantly memorable choruses and soaring toplines. The interplay between Nick’s lithe vocal and Joe’s angular yelp adds a hint of tension to the more upbeat songs and ardor to the slower ones, a contrast that was audible even with the screaming along of the fans in the Garden’s packed rafters.

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Jonas Brothers

With Bebe Rexha, Jordan McGraw

At TD Garden, Saturday; they return to TD Garden Nov. 24


Maura Johnston can be reached at maura@maura.com.