The common difference of the A.P. : $\dfrac{1}{3}, \dfrac{(1 − 3p)}{3}, \dfrac{(1 − 6p)}{3}$, … is:

1. p

2. −p

3. $\dfrac{1}{3}$

4. $\dfrac{-1}{3}$

The next term of the A.P. $\sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}$, … is:

1. $\sqrt{72}$

2. $\sqrt{68}$

3. $\sqrt{75}$

4. $\sqrt{56}$

The nth term of the A.P. $\dfrac {1}{m}, \dfrac{(1 + m)}{m}, \dfrac{(1 + 2m)}{m}$, … is:

1. $\dfrac{m(n − 1) + 1}{m}$

2. $\dfrac{m(n + 1) − 1}{m}$

3. $\dfrac{m(n − 1) − 1}{m}$

4. None of these

For what value of p are 2p + 1, 13, 5p − 3 three consecutive terms of an A.P. ?

1. 0

2. 1

3. 2

4. 4