Show that each of the progressions given below is an AP. Find the first term, common difference and next term of each.
√20, √45, √80, √125,…
Here, T2 - T1 = √45 - √20
= 3√5 - 2√5
= √5
T3 - T2 = = √80 - √45
= 4√5 - 3√5
= √5
T4 - T3 = = √125 - √80
= 5√5 - 4√5
= √5
Since the difference between each consecutive term is same, ∴ the progression is an AP.
So, first term = √20
Common difference = √45 - √20 = √5
Next term = T5 = T4 + d
= √125 + √5
= 5√5 + √5
= 6√5
= √180