Q. 244.4( 41 Votes )

Which term of the AP 121, 117, 113, ... is its first negative term?

Answer :

Here, First term = a = 121

Common difference = d = 117 - 121 = - 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


121 + (n - 1) × (-4) < 0


- 4n + 125 < 0


- 4n < - 125


4n > 125


n > 31.25


Since n is an integer, therefore n must be 32.


32nd term will be the first negative term of the AP.


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