KnowledgeBoat Logo
|

Mathematics

Observe the sequence of the terms : 3, 8, 13, …………..

Assertion (A): 53 is a term of this A.P.

Reason (R): Its first term is 3 and common difference is 5.

  1. Assertion (A) is true, but Reason (R) is false.

  2. Assertion (A) is false, but Reason (R) is true.

  3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

  4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

A.P.

3 Likes

Answer

Given sequence: 3, 8, 13, …………..

First term = 3

Difference between second and first term :

⇒ a2 - a1 = 8 - 3 = 5

Difference between third and second term :

⇒ a3 - a2 = 13 - 8 = 5

Thus, the above sequence is an A.P. with first term (a) = 3 and common difference (d) = 5.

So, reason (R) is true.

By formula,

an = a + (n - 1)d

If 53 is a term of this A.P., then

⇒ 53 = 3 + (n - 1)5

⇒ 53 - 3 = (n - 1)5

⇒ 50 = (n - 1)5

⇒ n - 1 = 505\dfrac{50}{5}

⇒ n - 1 = 10

⇒ n = 10 + 1 = 11.

Thus, 53 is 11th term of the A.P.

So, assertion (A) is true.

Thus, both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

Hence, option 3 is the correct option.

Answered By

1 Like

Related Questions