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Assume three numbers in AP are a-d, a, a+d.
ATQ
a -d + a + a+d = 37
3a = 37
a = 37/3 = 12.333
a(a-d)(a+d) = 405
a(a2 -d2 ) = 405
12.33(152.11 -d2 ) = 405
d2 = 119.27
d = 10.92
Hence the numbers are 1.41, 12.33, 23.25.