Question

Three numbers form a geometric progression. if 4 is subtracted from the third term, then the three numbers will form an arithmetic progression. if, after this, 1 is subtracted from the second and third terms of the progression, then it will again result in a geometric progression. find these three numbers.

Answer 1

The three numbers are 1, 3, 9
A geometric progression is a sequence or progression of numbers having a common ratio. It is where the first number is multiplied by the common ratio and the answer would be the second number.Then multiply the second number to the common ratio to create the third number and so on.
While an arithmetic progression is a sequence or progression of numbers having the common difference. It is where the first number is added to the common difference and the answer would become the second number. The second number would be added to the common difference to create a third number and so on.
x1, x2, x3 is a geometric expression1, 3, 9   having the common ratio 3
x1, x2, x3-4 will become an arithmetic progression1, 3, 5   having the common difference 2
From the answer above, subtract 1 from the second and the third term, it will become a geometric expression again.1, 2, 4    having the common ratio 2