Find:

the 18th term of the AP √2, √18, √50, √98….

The given AP can be rewritten as √2, 3√2, 5√2, 7√2….

Here, First term = a = √2

Common difference = d = 3√2 - √2 = 2√2

To find = 18^th term, ∴ n = 18

Using the formula for finding n^th term of an A.P.,

a_n = a + (n - 1) × d

∴ a_n = √2 + (18 - 1) × 2√2

⇒ a_n = √2 + 17 × 2√2 = √2 + 34√2 = 35√2

∴ 18^th term of the given AP is 35√2.