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Mathematics

Which term of the A.P. 30, 27, 24, 21, ….. is the first negative term ?

  1. 10th

  2. 11th

  3. 14th

  4. 12th

AP GP

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Answer

Given,

A.P. = 30, 27, 24, 21, …..

In A.P.,

First term (a) = 30, Common difference (d) = 27 - 30 = -3.

Let nth term be the first negative term of the A.P.

∴ an < 0

⇒ a + (n - 1)d < 0

⇒ 30 + (n - 1)(-3) < 0

⇒ 30 - 3n + 3 < 0

⇒ 3n > 33

⇒ n > 333\dfrac{33}{3}

⇒ n > 11.

⇒ n = 12.

Hence, Option 4 is the correct option.

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