A.P.: ( 30, 29.5, 29, \ldots )

( a = 30 ), ( d = -0.5 )

We need the first negative term: [ a_n < 0 ] [ 30 + (n-1)(-0.5) < 0 ] [ (n-1)(-0.5) < -30 ] [ n-1 > 60 \quad (\text{inequality reverses when dividing by negative}) ] [ n > 61 ]

So the first negative term is the 62nd term.

Check: [ a_{62} = 30 + 61\cdot(-0.5) = 30 - 30.5 = -0.5 < 0 ] [ a_{61} = 30 + 60\cdot(-0.5) = 30 - 30 = 0 \quad (\text{not negative}) ]

Answer: 62nd term