Question

sum of the first two of a decreasing G.P is 5/4 and sum of infinite terms is 9/4,find the common ratio and the first term​

Answer 1

Answer:

Given:-

S  

∞

​  

=4

a  

2

​  

=  

4

3

​  

 

⇒ar=  

4

3

​  

 

⇒4ar=3.....(1)

As we know that,

S  

∞

​  

=  

1−r

a

​  

 

∴  

1−r

a

​  

=4

⇒4r=4−a.....(2)

From equation (1)&(2), we have

a(4−a)=3

⇒a  

2

−4a+3=0

⇒(a−3)(a−1)=0

⇒a=1 or a=3

Substituting the value of a in equation (1), we get

For a=3

⇒r=  

4

1

​  

 

For  a=1

⇒r=  

4

3

​

Explanation:

Answer 2

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S  

∞

 

=4

a  

2

 

=  

4

3

 

 

⇒ar=  

4

3

 

 

⇒4ar=3.....(1)

As we know that,

S  

∞

 

=  

1−r

a

 

 

∴  

1−r

a

 

=4

⇒4r=4−a.....(2)

From equation (1)&(2), we have

a(4−a)=3

⇒a  

2

−4a+3=0

⇒(a−3)(a−1)=0

⇒a=1 or a=3

Substituting the value of a in equation (1), we get

For a=3

⇒r=  

4

1

 

 

For  a=1

⇒r=  

4

3