Answer :

The given arithmetic progression is √2, 3√2, 5√2, …
Its first term a = √2
Common difference = d = 3√2 – √2 = 2√2.
So nth term an of the given arithmetic progression is given by
an = a + (n -1)d


Where,


a = First term of AP
d = Common difference of AP
and no of terms is ‘n’



Thus 18th term a18 = √2 + (18 - 1) × 2√2.
a18 = √2 + 17 × 2√2 = √2 + 34√2 = 35√2


Hence, 18th term is 35√2.


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