Q8 of 24 Page 115

Find the 10th term of the sequence √2, √8, √18.......

Given Sequence,


√2,√8,√18,…


⇒√2, 2√2, 3√2, …


Let us find the difference of consecutive terms,


a2 – a1 = 2√2 – √2 = √2


a3 – a2 = 3√2 – 2√2 = √2


As consecutive differences of terms are same, therefore above series is an AP with


First term, a = √2


Common difference, d = √2


We know, nth term of an AP is


an = a + (n – 1)d


⇒ a10 = √2 + (10 – 1)√2


⇒ a10 = √2 + 9√2


⇒ a10 = 10√2


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