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Mathematics

Which term of the A.P. 18, 15, 12, ………… is the first negative term ?

  1. 6th

  2. 8th

  3. 7th

  4. 5th

AP GP

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Answer

A.P. = 18, 15, 12, …………

Common difference (d) = 15 - 18 = -3

First term (a) = 18

Let nth term be the first negative term.

⇒ an < 0

⇒ a + (n - 1)d < 0

⇒ 18 + (n - 1)(-3) < 0

⇒ 18 - 3n + 3 < 0

⇒ 21 - 3n < 0

⇒ 3n > 21

⇒ n > 213\dfrac{21}{3}

⇒ n > 7

⇒ n = 8.

Hence, Option 2 is the correct option.

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