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Which Term of the Progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the First Negative Term? - Mathematics

Which term of the progression 20, 19`1/4`,18`1/2`,17`3/4`, ... is the first negative term?

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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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