Question

which term of the g.p 1/3,1/9,1/27,...is 1/2187?

Answer 1

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Answer 2

Answer:

7th term of the G.P is $\frac{1}{2187}$    

Step-by-step explanation:

Given : G.P $\frac{1}{3}, \frac{1}{9}, \frac{1}{27},....$

To find : Which term of the G.P is $\frac{1}{2187}$ ?

Solution :

G.P $\frac{1}{3}, \frac{1}{9}, \frac{1}{27},....$

Here, first term is $a=\frac{1}{3}$

Common ratio is $r=\frac{\frac{1}{9}}{\frac{1}{3}}$

$r=\frac{1}{3}$

The nth term of GP is $a_n=\frac{1}{2187}$

The nth term of GP is $a_n=ar^{n-1}$

Substitute the value,

$\frac{1}{2187}=(\frac{1}{3})(\frac{1}{3})^{n-1}$

$\frac{3}{2187}=(\frac{1}{3})^{n-1}$

$\frac{1}{729}=(\frac{1}{3})^{n-1}$

$(\frac{1}{3})^6=(\frac{1}{3})^{n-1}$

Compare the base,

$6=n-1$

$n=7$

Therefore, 7th term of the G.P is $\frac{1}{2187}$