Math, asked by asmaqadri179, 6 months ago

In a sequence if an=5(3^n-1).prove that it is a GP.find the first term and the common ratio​

Answers

Answered by magician340104
0

Step-by-step explanation:

ANSWER

Given,

S

n

=

3

n

4

n

−3

n

⇒S

n

=(

3

4

)

n

−1

S

n−1

=(

3

4

)

n−1

−1

T

n

=S

n

−S

n−1

=(

3

4

)

n

−1−(

3

4

)

n−1

+1

=(

3

4

)

n−1

(

3

4

−1)

∴T

n

=

4

1

(

3

4

)

n

T

1

=

4

1

(

3

4

)

1

=

3

1

T

2

=

4

1

(

3

4

)

2

=

9

4

T

3

=

4

1

(

3

4

)

3

=

27

16

T

1

T

2

=

9

4

×

1

3

=

3

4

T

2

T

3

=

27

16

×

4

9

=

3

4

As

T

1

T

2

=

T

2

T

3

, given series is in G.P

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