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