Question

and sixth
Ex 4) In a G.P. ,if the third term is 1/5 and sixth term is 1/625 , find its nth term.
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Answer 1

The nth term of G.P is $a_n=5(\frac{1}{5})^{n-1}$.

Step-by-step explanation:

Given :  In a G.P. if the third term is 1/5 and sixth term is 1/625.

To find : Its nth term ?

Solution :

The nth term of G.P. is $a_n=ar^{n-1}$

The third term of G.P is given by,

$ar^2=\frac{1}{5}$  ......(1)

The sixth term of G.P is given by,

$ar^5=\frac{1}{625}$  ......(2)

Divide (1) and (2),

$\frac{ar^5}{ar^2}=\frac{\frac{1}{625}}{\frac{1}{5}}$

$r^3=\frac{1}{125}$

$r^3=\frac{1}{5^3}$

$r=\frac{1}{5}$

Substitute r in (1),

$a(\frac{1}{5})^2=\frac{1}{5}$

$\frac{a}{25}=\frac{1}{5}$

$a=5$

The first term is a=5 and common ratio is r=\frac{1}{5}

The nth term of G.P is

$a_n=5(\frac{1}{5})^{n-1}$

#Learn more

In a G.p first term is 4 and third term is 144 find the G.p and the sum of first four term?

https://brainly.in/question/12096620

Answer 2

Answer:

yes

Step-by-step explanation:

yes upper answer is right answer