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Mathematics

Assertion (A) : 205 is not a term of the sequence 8, 12, 16, 20, ……

Reason (R) : The number of terms of every sequence is never in fraction.

  1. A is true, R is false.

  2. A is false, R is true.

  3. Both A and R are true.

  4. Both A and R are false.

AP GP

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Answer

A.P. : 8, 12, 16, 20, ……….

In the above A.P. :

⇒ a = 8

⇒ d = 12 - 8 = 4

Let 205 be nth term of the sequence.

⇒ an = a + (n - 1)d

⇒ 205 = 8 + 4(n - 1)

⇒ 205 - 8 = 4(n - 1)

⇒ 197 = 4(n - 1)

⇒ n - 1 = 1974\dfrac{197}{4}

⇒ n - 1 = 491449\dfrac{1}{4}

⇒ n = 4914+149\dfrac{1}{4} + 1

⇒ n = 501450\dfrac{1}{4}

Since, term cannot be in fraction.

∴ 205 is not a term of the sequence 8, 12, 16, 20, ……

∴ Assertion (A) is true.

We know that,

In a sequence the number of terms are never in fraction.

∴ Reason (R) is true.

Hence, Option 3 is the correct option.

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