Question

given that Nam's are inserted between two sets of numbers a,2b and 2a,b where a,bER further nth mean between these sets of numbers is same then ratio of a:b

Answer 1

Answer:

a:b=n:1

Step-by-step explanation:

a,2b

If n means are inseted then

first term=a and n+2 th term=2b

so 2b=a+(n+2-1)d

d=(2b-a)/(n+1)

So nth mean =n+1 th term

= a+n*(2b-a)/(n+1)

Similarly nth mean between 2a and b is:

=2a+n(b-2a)/(n+1)

As per question

2a+n(b-2a)/(n+1) = a+n*(2b-a)/(n+1)

a =n*(2b-a)/(n+1)-n(b-2a)/(n+1)

a=n/(n+1) { 2b-a-b+2a)

a(n+1) =n(a+b)

an+a=na+nb

a=nb

a:b=n:1