Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.

√2, √8, √18, √32,…

Here, T₂ - T₁ = √8 - √2

= 2√2 - √2

= √2

T₃ - T₂ = = √18 - √8

= 3√2 - 2√2

= √2

T₄ - T₃ = = √32 - √18

= 4√2 - 3√2

= √2

Since the difference between each consecutive term is same, ∴ the progression is an AP.

So, first term = √2

Common difference = √8 - √2 = √2

Next term = T₅ = T₄ + d

= √32 + √2

= 4√2 + √2

= 5√2

= √50