Three positive numbers are in arithmetic progression. When 1 is added to each of them, the resulting numbers are in geometric progression.
(i) If the original numbers are a−d,a,a+d with a>0 and d>0, write the algebraic relations implied by the given condition.
(ii) Solve these relations to find all possible ordered triples of positive numbers that satisfy the stated property.
(iii) Among the triples obtained in part (ii), indicate which ones form an increasing sequence and justify your answer.