Given GP is 2, 2√2, 4, 8√2 …..

The given GP is of the form, a, ar, ar², ar³….

Where r is the common ratio.

First term in the given GP, a₁ = a = 2

Second term in GP, a₂ = 2√2

Now, the common ratio,

Now, n^th term of GP is, a_n = ar^{n – 1}

So, the 17^th term in the GP,

a₁₇ = ar¹⁶

= 2 x (√2)¹⁶

= 512

n^th term in the GP,

a_n = ar^{n – 1}

= 2(√2) ^{n – 1}

= (√2) ^{n + 1}

Hence, 17^th term = 512 and n^th term = (√2) ^{n + 1}