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Question
Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?
Solution
The given sequence is 20, 19`1/4`,18`1/2`,17`3/4`,...
First term, a = 20
Common difference, d = `19 1/4 - 20 = (77 - 80)/4 = -3/4`
Let the nth term of the AP be the first negative term
So `a_n < 0`
`=> a + (n - 1)d < 0`
`=>20 + (n - 1)(-3/4) < 0`
`=> 83/4 - (3n)/4 < 0`
`=> 83 - 3n < 0`
`=> 3n > 83`
`=> n > 27 2/3`
`=> n >= 28`
Thus, the 28th term is the first negative term of the given AP
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