Q13 of 24 Page 115

Which term of the A. P. 84, 80, 76.... is zero?

Let the first term of AP be ‘a’ and common difference be ‘d’.


For given AP,


a = 84


d = a2 – a = 80 – 84 = –4


We know, nth term of an AP is


an = a + (n – 1)d


Now, let the nth term be 0 then


0 = 84 + (n – 1)(–4)


⇒ –84 = –4(n – 1)


⇒ n – 1 = 21


⇒ n = 22


Hence, 22th term of given AP is 0.


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