Q21 of 178 Page 559

Which term of the AP 25, 20, 15, ... is the first negative term?

In the given AP, the first term = a = 25


Common difference = d = 20 - 25 = - 5


To find: place of first negative term.


So, an < 0


Since, we know that


an = a + (n - 1) × d


∴ 25 + (n - 1) × (-5) < 0


⇒ 25 - 5n + 5 < 0


⇒ - 5n + 30 < 0


⇒ - 5n < - 30


⇒ 5n > 30


⇒ n > 6


∴ 7th term of the AP is the first negative term.

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