3 numbers form an arithmetic sequence with a common difference of 11. If the first number....

Question

           Three numbers form an arithmetic sequence with a common difference of 11. If the first number is decreased by 6, the second number is decreased by 1 and the third number is doubled, these three new numbers would form a geometric sequence. Determine the first three terms of the original arithmetic sequence. 

Answer 1

If 3 numbers form an arithmetic sequence with a common difference of 11 then the 3 numbers are  

 

X, X+11, X+22  

 

If the first is decreased by 6, the second is decreased by 1 and the third is doubled then the 3 new numbers are  

 

X-6, X+10, 2X+44  

 

If these 3 new numbers form a geometric sequence then the successive terms have a common ratio, which means  

 

(X+10)/(X-6) = (2X+44)/(X+10)  

 

Solve for X