Question

Which term of G. P. 1, 1/2, 1/4 ,1/8 ..........will be 1/512?

Answer 1

Answer:

Step-by-step explanation:

We know n th tuem of g.p is a base n=ar^n-1

Now here a base n is 1 /512 and a=1 and r=1/2 then

1/512=1 into (1/2)^n-1

1/(2)^9=1/(2)^n-1

Here is doing comparison then

(2)^9=(2)^n-1 and n-1=9

n=9+1=10 so 10th will be 1/512

Answer 2

Answer:

If the GP is 1, 1/2, 1/4, 1/8.... then, 1/512 is the tenth term of the GP

Step-by-step explanation:

Given

The GP 1, 1/2, 1/4, 1/8....

Here,

First term a = 1

Common ration r = 1/2 ÷1 = 1/2

For a GP , nth term is

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

Here, nth term an = 1/512

Substitute the values for $a_{n}$, a and r

So,

$\frac{1}{512} = 1*\frac{1}{2}^{(n-1)}$

$\frac{1}{512} = \frac{1}{2}^{(n-1)}$

$512 = (2)^{9}$

So,

$\frac{1}{512} = \frac{1}{2}^{(9)}$

So,

$\frac{1}{2}^{(9)} = \frac{1}{2}^{(n-1)}$

So, n-1 = 9

n = 9+1 = 10

So, 1/512 is the 10 th term of the GP