Q. 1 D4.0( 15 Votes )

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,…

Answer :

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


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