Verify that each of the following is an AP and then write its next three terms.
(i) `0, (1)/(4),(1)/(2),(3)/(4), … " " ` (ii) `5,(14)/(3),(13)/(3),4, …`
(iii) `sqrt(3),2sqrt(3),3sqrt(3), … " " ` (iv) `a+b,(a+1)+b,(a+1)+(b+1), ...`
(v) `a,2a+1,3a+2,4a+3, …`

Explanation

To verify that each of the given sequences is an Arithmetic Progression (AP) and to find the next three terms, we will follow these steps:

### (i) Sequence: \(0, \frac{1}{4}, \frac{1}{2}, \frac{3}{4}, \ldots\)

1. **Find the common difference \(D\)**:
- \(D_1 = \frac{1}{4} - 0 = \frac{1}{4}\)
- \(D_2 = \frac{1}{2} - \frac{1}{4} = \frac{2}{4} - \frac{1}{4} = \frac{1}{4}\)
- \(D_3 = \frac{3}{4} - \frac{1}{2} = \frac{3}{4} - \frac{2}{4} = \frac{1}{4}\)
...