Question

3 arithmetic means a1, a2 and a3 are inserted between x and y. if the arithmetic means b1, b2, b3, b4 and b5 are inserted between x and y, then (a2-a1)/(b5-b4) is​

Answer 1

Step-by-step explanation:

Given :-

3 arithmetic means a1, a2 and a3 are inserted between x and y. if the arithmetic means b1, b2, b3, b4 and b5 are inserted between x and y

To find :-

Find the value of (a2-a1)/(b5-b4) ?

Solution :-

Given that

3 arithmetic means b1, b2, b3, b4 are inserted between x and y.

The AP :x,a1,a2,a3,y

Number of arithmetic means = 3

n = 3

We know that

If n arithmetic means are between a and b then Common difference (d) = (b-a)/(n+1)

So, The common difference = (x-y)/(3+1)

=>d = (x-y)/4 -----------(1)

=>d = a2-a1 = a3-a2

if the arithmetic means b1, b2, b3, b4 and b5 are inserted between x and y

The AP :x,b1, b2, b3, b4,b5,y

Number of arithmetic means = 5

n= 5

=> Common difference = (x-y)/(5+1)

=> d = (x-y)/6 -----------(2)

=>d = b2-b1 = b3-b2=b4-b3 = b5-b4

Now,

(a2-a1)/(b5-b4)

=> [(x-y)/4]/[(x-y)/6]

=>[(x-y)/4]×[6/(x-y)]

=> 6(x-y)/4(x-y)

=> 6/4

=> 3/2

Answer:-

The value of (a2-a1)/(b5-b4) for the given problem is 3/2

Used formulae:-

If n arithmetic means are between a and b then Common difference (d) = (b-a)/(n+1)

a = first term

b = last term

n = number of arthmetic means