Question

Assertion: 2 + 4 + 6 + 8 + ... + 50 = 650

Reason: Sum of n terms of A.P. `n/2[2a + (n - 1)d]`.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).

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

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

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

Explanation:

a = 2, d = 2 and l = 50

n = 50 = 2 + (n − 1)2

⇒ 50 − 2 = (n − 1)2

⇒ 48 = (n − 1)2

⇒ `48/2 = n − 1`

⇒ 24 + 1 = n

⇒ n = 25

`S_n = n/2[2a + (n - 1)d]`

`S_25 = 25/2[2(2) + (25 - 1)2]`

`S_25 = 25/2[4 + (24)2]`

`S_25 = 25/2[4 + 48]`

`S_25 = 25/2[52]`

`S_25 = 25 × 26`

S₂₅ = 650