Question

If the sum of 40 arithmetic mean between two numbers is 120, then the sum of 50 arithmetic mean between them is equal to

Answer 1

HELLO DEAR,

Let A1, A2, A3, ........ , A40 be 40 A.M's between two numbers 'a' and 'b'.

Then, 

a, A1, A2, A3, ........ , A40, b is an A.P. with common difference d  = (b - a)/(n + 1) = (b - a)/41
[ where n = 40]

now,

A1, A2, A3, ........ , A40  = 40/2( A1 + A40)

A1, A2, A3, ........ , A40 = 40/2(a + b)
[ a, A1, A2, A3, ........ , A40, b is an Ap then ,a + b = A1 + A40]

sum of 40A.M = 120(given)

120= 20(a + b)

=> 6 = a + b ----------(1)

Again ,
consider B1, B2, ........ , B50  be 50 A.M.'s between two numbers a and b.

Then, a, B1, B2, ........ , B50, b will be in A.P. with common difference = ( b - a)/51

now , similarly,

B1, B2, ........ , B50 = 50/2(B1 + B2)

= 25(6) ----------------from(1)

= 150

I HOPE ITS HELP YOU DEAR,
THANKS