Question

find 20th term of the gp 1/3, 1/9, 1/27​

Answer 1

Answer:

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Step-by-step explanation:

Answer:

7th term of the G.P is \frac{1}{2187}21871    

Step-by-step explanation:

Given : G.P \frac{1}{3}, \frac{1}{9}, \frac{1}{27},....31,91,271,....

To find : Which term of the G.P is \frac{1}{2187}21871 ?

Solution :

G.P \frac{1}{3}, \frac{1}{9}, \frac{1}{27},....31,91,271,....

Here, first term is a=\frac{1}{3}a=31

Common ratio is r=\frac{\frac{1}{9}}{\frac{1}{3}}r=3191

r=\frac{1}{3}r=31

The nth term of GP is a_n=\frac{1}{2187}an=21871

The nth term of GP is a_n=ar^{n-1}an=arn−1

Substitute the value,

\frac{1}{2187}=(\frac{1}{3})(\frac{1}{3})^{n-1}21871=(31)(31)n−1

\frac{3}{2187}=(\frac{1}{3})^{n-1}21873=(31)n−1

\frac{1}{729}=(\frac{1}{3})^{n-1}7291=(31)n−1

(\frac{1}{3})^6=(\frac{1}{3})^{n-1}(31)6=(31)n−1

Compare the base,

6=n-16=n−1

n=7n=7

Therefore, 7th term of the G.P is \frac{1}{2187}21871