Given: GP is 2, 6, 18, 54….

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 = 6

Now, the common ratio,

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

So, the 6^th term in the GP,

a₆ = ar⁵

= 2 x 3⁵

= 486

n^th term in the GP,

a_n = ar^{n – 1}

= 2.3^{n – 1}

Hence, 6^th term = 486 and n^th term = 2.3^{n – 1}