# Which Term of the Progression 20, 191/4,181/2,173/4, ... is the First Negative Term? - Mathematics

Which term of the progression 20, 191/4,181/2,173/4, ... is the first negative term?

#### Solution

The given sequence is 20, 191/4,181/2,173/4,...

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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