Question

find the common ratio of G p 1-1/3+1/9-1/27+------------​

Answer 1

Answer:

Given series

1

,

1

3

,

1

9

,

1

27

,

...

is a G.P. with the first term

a

=

1

& common ratio

r

=

1

3

1

=

1

9

1

3

=

1

27

1

9

=

...

=

1

3

Now, the sum of given series up to

n

=

10

terms

=

a

(

r

n

−

1

)

r

−

1

=

1

(

(

1

3

)

10

−

1

)

1

3

−

1

=

(

1

3

)

10

−

1

−

2

3

=

3

2

(

1

−

(

1

3

)

10

)

≈

1.499974597

Answer 2

The common ratio is $- \frac{1}{3}$

Given:

A GP 1, -1/3, +1/9, -1/27+------------

To Find:

The common ratio.

Solution:

To find the common ratio we will follow the following steps:

As we know,

The given series is forming a GP and the ratio of successive numbers is the same.

GP = -1/3, +1/9, -1/27+------------

Now,

$First \: term = \frac{ - 1}{3}$

$Second \: term = \frac{ + 1}{9}$

$Third \: term = \frac{ - 1}{27}$

Now,

Common ratio =

$\frac{second term }{first \: term} = \frac{third \: term }{second\: term}$

So,

Common ratio =

$\frac{ \frac{1}{9} }{ - \frac{1}{3} } = \frac{ - \frac{1}{27} }{ \frac{1}{9} } = \frac{ - 1}{3}$

Henceforth, the common ratio is $- \frac{1}{3}$

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