Question

For the following G.P.s find $t_{n}$.
i) 3, 15, 75, 375, ...
ii) 1, -4, 16, -64, ...
iii) 1, -3/2, 9/4, -27/8, ....
iv) $\sqrt{3}, \frac{1}{\sqrt{3}}, \frac{1}{3\sqrt{3}},\frac{1}{9\sqrt{3}},...$

Answer 1

Answer:

Step-by-step explanation:

Concept:

The n th term of G.P

a, ar, $ar^2,ar^3$........... is

$t_{n}=ar^{n-1}$

1.

3, 15, 75............

Here, a = 3, r = 5

$t_{n}=ar^{n-1}\\\\t_{n}=3(5)^{n-1}$

2.

1, -4, 16............

Here, a = 1, r = -4

$t_{n}=ar^{n-1}\\\\t_{n}=1(-4)^{n-1}\\\\t_{n}=(-4)^{n-1}$

3.

1, -3/2, 9/4...........

Here, a = 1, r = -3/2

$t_{n}=ar^{n-1}\\\\t_{n}=1(\frac{-3}{2})^{n-1}\\\\t_{n}=(\frac{-3}{2})^{n-1}$

4.

$\sqrt{3}, \frac{1}{\sqrt{3}},\frac{1}{3\sqrt{3}}$.................

$a=\sqrt{3}, r=\frac{1}{3}\\\\t_{n}=ar^{n-1}\\\\t_{n}=\sqrt{3}(\frac{1}{3})^{n-1}$