In a geometric progression consisting of positive terms, each term equals the sum of the next two terms. Then, the common ratio of this progression equals
The explanation for the correct option
Let us assume that the first term of the geometric progression is and the common ratio is .
Thus, the first three terms of the progression can be given by , and .
It is given that each term equals the sum of the next two terms.
The solution to the quadratic equation can be given by, .
Therefore, the solution for the equation is .
As the progression consists only of positive terms, therefore, the common ratio of the progression, .
Hence, (D) is the correct option.