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

1.	Find the 7th and nth terms of the GP 0.4, 0.8, 1.6….
Answer» 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

Answer»

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

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