"increasingly large number" is correct and usable in written English.
You can use it when you are referring to a quantity or amount that is growing or increasing. For example, "The shop has seen an increasingly large number of customers over the past few months."
"We have an increasingly large number of students interested in technology and art," she says.
An increasingly large number of visitors come specifically to see contemporary art.
And an increasingly large number are starting to customize jet skis in a similar hot-rod style.
The former British Army colonel's unique job is to hunt for illegal gold miners, an increasingly large number of them who work the ground at night.
Such works were completed at a time when books—some of which were still being hand-copied were soughand-copied wereingly large number of readersought
Cuts to legal aid, declines in state funding and lawyers' high fees have already rendered the county courts that deal with smaller claims inhospitable for an increasingly large number of unrepresented litigants.
It is hardly surprising that the increasingly large number of French people who vote for the FN regard this as a way of cheating them of the victory that would otherwise have been theirs.
Despite being derided by some as Gove's puppet, Wilshaw has spoken sceptically of some of the education reforms initiated under Gove, particularly the growth of academy chains that manage an increasingly large number of state schools in England.
Beginning in the 1990s, new forums for exhibition, such as the Montenegro Cetinje Biennial, allowed work by Montenegrin artists to be seen by an increasingly large number of people.
The tourist industry has grown rapidly since the 1960s, with an increasingly large number of French families taking a holiday each year, encouraged by greater affluence, more leisure time, and, since 1982, five weeks' statutory paid holiday.
It matters for an increasingly large number of uses, as more business takes place on the Internet, and more data than old systems were ever designed for is collected in the normal course of business.
