Answer:
The numbers are 6, 18, and 30
Step-by-step explanation:
If the three numbers are in the ratio of 3:9:10,
let the numbers be 3x, 9x and 10x.
If 10 is added to the last number to form an arithmetic progression
Then, 3x 9x (10x+10) are the progression
The common difference of an arithmetic progression (d) = T₂ - T₁ = T₃ - T₂
T₂-T₁ = T₃ - T₂ .............. Equation 1
Where T₁ = first term of the progression, T₂ = Second term of the progression, T₃ = third term of the progression
Given: T₁ = 3x, T₂ = 9x, T₃ = 10x +10
Substituting these values into equation 1
9x-3x = (10x+10)-9x
Solving the equation above,
3x = 10+x
3x-x = 10
2x = 10
x = 10/2
x = 2.
Therefore the numbers are 6, 18, and 30
