Find the 7^th and nth terms of the GP 0.4, 0.8, 1.6….

Given GP is 0.4, 0.8, 1.6….

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 = 0.4

Second term in GP, a₂ = 0.8

Now, the common ratio,

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

So, the 7^th term in the GP,

a₇ = ar⁶

= 0.4 x 2⁶

= 25.6

n^th term in the GP,

a_n = ar^{n – 1}

= (0.4)(2) ^{n – 1}

= (0.2)2ⁿ

Hence, 7^th term = 25.6 and n^th term = (0.2)2ⁿ