Assertion (A): Sum of first n terms of the AP 3, 13, 23 … is

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Q.
Assertion (A): Sum of first n terms of the AP 3, 13, 23 … is $5 n^{2} - 8 n$ .

Reason (R): The sum of first n terms of an AP is given by $S_{n} = n / 2 [2 a + (n - 1) d]$

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.

Ans.
(4)

We have AP 3, 13, 23, … Here,

a = 3, d = 13 – 3 = 10

$∴ S_{n} = \frac{n}{2} (2 a + (n - 1) d) = \frac{n}{2} (2 \times 3 + (n - 1) \times 10) = n (3 + (n - 1) \times 5) \Rightarrow S_{n} = n (5 n - 2) = 5 n^{2} - 2 n$

Solution

Q.
Assertion (A): Sum of first n terms of the AP 3, 13, 23 … is $5 n^{2} - 8 n$ .

Reason (R): The sum of first n terms of an AP is given by $S_{n} = n / 2 [2 a + (n - 1) d]$

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.

Ans.
(4)

We have AP 3, 13, 23, … Here,

a = 3, d = 13 – 3 = 10

$∴ S_{n} = \frac{n}{2} (2 a + (n - 1) d) = \frac{n}{2} (2 \times 3 + (n - 1) \times 10) = n (3 + (n - 1) \times 5) \Rightarrow S_{n} = n (5 n - 2) = 5 n^{2} - 2 n$

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Solution

Q. Assertion (A): Sum of first n terms of the AP 3, 13, 23 … is 5n2-8n. Reason (R): The sum of first n terms of an AP is given by Sn=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.

Ans. (4) We have AP 3, 13, 23, … Here, a = 3, d = 13 – 3 = 10 ∴ Sn=n2(2a+(n-1)d)=n2(2×3+(n-1)×10)=n(3+(n-1)×5)⇒ Sn=n(5n-2)=5n2-2n

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Q.
Assertion (A): Sum of first n terms of the AP 3, 13, 23 … is $5 n^{2} - 8 n$ .

Reason (R): The sum of first n terms of an AP is given by $S_{n} = n / 2 [2 a + (n - 1) d]$

Ans.
(4)

We have AP 3, 13, 23, … Here,

a = 3, d = 13 – 3 = 10

$∴ S_{n} = \frac{n}{2} (2 a + (n - 1) d) = \frac{n}{2} (2 \times 3 + (n - 1) \times 10) = n (3 + (n - 1) \times 5) \Rightarrow S_{n} = n (5 n - 2) = 5 n^{2} - 2 n$