The first three terms of an arithmetric progression are x, 2x +y and 9x - y. The sum of these three terms is 60. Find the value of x and y. Then, calculate the eleventh term of the progression.

Answer 1

Let d = common difference, Then:

2x + y = x + d

9x - y = x + 2d

x + (x+d) + (x+3d) = 60

So, 3x + 3d = 60.

Therefore, x + d = 20

Substituting, we get:

2x + y = 20

9x - y = 40 - x

2x + y = 20

10x - y = 40

12x = 60

So, x = 5 and d = 15 and y = 10

Eleventh term = x + 10d = 155