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The Arizona State Quarter comes out next. New Mexico was the last one and after Arizona, Alaska comes out.
Assuming you mean a quarter that is normally struck, but is missing the outer silvery-colored layer ... If it is a state quarter, these have been selling in the $300-$400 range. If it is an older quarter, these have been selling for about $50
The words "United States of America" and "Quarter Dollar" typically appear on the front (obverse) of a quarter. The specific design and additional words may vary depending on the commemorative or state quarter.
If the two dates are 1776 & 1976 It's a bicentennial quarter and it's still worth a quarter If it's a state or territorial quarter, has two dates on the back and one of them is between 1999 and 2009 it's also just worth a quarter. If it has two heads with a date on each side it's a magician's coin - see the Related Question.
Unless the quarter is in mint-state or a proof, the value would be the melt value of the silver in the coin which is $3.80ish as of this time of writing, but changes depending on the spot price of silver.