Show that each of the progressions given is an AP. Find the first term , common difference and next term of given series
`(iii) sqrt2 ,sqrt8 , sqrt(18) ,sqrt(32) . . . `

Explanation

To show that the given series \( \sqrt{2}, \sqrt{8}, \sqrt{18}, \sqrt{32} \) is an arithmetic progression (AP), we need to find the common difference between consecutive terms and verify that it is constant.

### Step 1: Identify the terms
Let:
- \( a_1 = \sqrt{2} \)
- \( a_2 = \sqrt{8} \)
- \( a_3 = \sqrt{18} \)
- \( a_4 = \sqrt{32} \)
...