Question

If the first and the nth terms of a G.P. are a and b

respectively and if P is the product of the first n

terms, prove that

2

( )n P ab  .​

Answer 1

Geometric progression

1  

st

 term =a

n  

th

 term =b

P= product of n terms

G.P.=a,ar,ar  

2

.....ar  

n−1

 

→b=ar  

n−1

 

→P=(a)(ar)(ar  

2

)...(ar  

n−1

)

→P=a  

n

(1×r×r  

2

×...r  

n−1

)

→P=a  

n

r  

(1+2+3+...+n+1)

 

→P=a  

n

r  

2

(n−1)n

​  

 

 

Now,  

→P  

2

=a  

2n

r  

n(n−1)

 

→P  

2

=(a  

2

r  

n−1

)  

n

 

→P  

2

=(a⋅b)  

n

 

Hence

P  

2

=(a⋅b)  

2

Answer 2

Answer:

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Step-by-step explanation: