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Mathematics

Assertion (A): For an A.P., T22 = 149 and d = 7. Then S22 is 1661.

Reason (R): The sum of first n terms of an A.P. is given by Sn = n2[2a−(n−1)d]\dfrac{n}{2}[2a − (n − 1)d].

  1. Both A and R are true, and R is the correct explanation of A.

  2. Both A and R are true, but R is not the correct explanation of A.

  3. A is true, but R is false.

  4. A is false, but R is true.

AP

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Answer

Given,

a22 = 149

n = 22

d = 7.

We know that,

⇒ an = a + (n - 1)d

⇒ a22 = a + (22 - 1)7

⇒ 149 = a + (21)7

⇒ 149 = a + 147

⇒ 149 - 147 = a

⇒ a = 2.

We know that,

Sn = n2\dfrac{n}{2} (a + l)

⇒ S22 = 222\dfrac{22}{2} (2 + 149)

= 11 × (151)

= 1661.

Assertion (A) is true.

The standard and correct formula for the sum of the first n terms of an A.P.

Sn = n2\dfrac{n}{2} [2a + (n − 1)d]

Reason (R) is false.

A is true, R is false

Hence, option 3 is the correct option.

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