Question

If x - 2y, 2x - y, 3x, ........., 11x + 8y are terms of an Arithmetic Progression,
then their sum is .....​

Answer 1

Soln: Let the numbers are x and y. One of them must be greater than or equal to the other. Let us assume that x is greater than or equal to y.

The sum of the two numbers is 8. Thus, we have x+y = 8

The sum of the two numbers is four times their difference. Thus, we have

x+y = 4(x— y)

=>x+y= 4x-4y

=>4x — 4y—x—y = 0

=> 3x-5y = 0

So, we have two equations

x+y=8

3x-5y = 0

Here x and y are unknowns.

We have to solve the above equations for x and y.

Multiplying the first equation by 5 and then adding with the second equation, we have

5(x + y)+(3x — 5y) = 5×8+0

=>5x+5y+3x-5y =40

=>8x = 40

=> x = 5

x = Substituting the value of x in the first equation, we have

5+y=8

=>y=8-5

=>y=3

Hence, the numbers are 5 and 3.