Q. 254.3( 25 Votes )

Which term of the AP is its first negative term?

Answer :

Here, First term = a = 20

Common difference = d = (77/4) - 20 = (-3/4)


Let nth term of the AP be its first negative term.


an <0


Since, nth term of an AP is given by:


an = a + (n - 1)d


a + (n - 1)d < 0


20 + (n - 1) × (-3/4) < 0


80 + (n - 1) × (-3) < 0 (multiplying both sides by 4)


80 - 3n + 3 < 0


- 3n < - 83


3n > 83


n > 27.66


Since n is an integer, therefore n must be 28.


28th term will be the first negative term of the AP.


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