Question

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

Answer 1

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, \(r = \frac{a_2}{a_1}\)

r = \(\frac{0.8}{0.4}\) = 2

Now, n^th term of GP is, an = 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, an = ar^{n – 1} = (0.4)(2)^{n – 1} 

= (0.2)2ⁿ 

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