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 n^{th} term a_{n} of the given arithmetic progression is given by

a_{n} = a + (n -1)d

Where,

a = First term of AP

d = Common difference of AP

and no of terms is ‘n’

Thus 18^{th} term a_{18} = √2 + (18 - 1) × 2√2.

⇒ a_{18} = √2 + 17 × 2√2 = √2 + 34√2 = 35√2

Hence, 18^{th} term is 35√2.

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