Question

if there are n gms between m and n then common ratio of gp is

Answer 1

Answer:

G.P. series of (n+2) terms:

a,G

1

,G

2

,..........,G

n

,b

Let r be the common ratio:

∴b=ar

n+1

⇒r=(

a

b

)

(n+1)

1

G is the single GM between a and b, so we have:

G=(ab)

2

1

The product G

1

×G

2

×...............×G

n

=a

n

×((

a

b

)

n+1

1

)

2

n(n+1)

=a

n

×(

a

b

)

2

n

=a

2

n

×b

2

n

=(ab)

2

n