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