In a geometric progression, the sum of the first and second terms is 75, and the sum of the second

In a geometric progression, the sum of the first and second terms is 75, and the sum of the second and third terms is 150. Find the first three terms of this progression.

Let the second term of the geometric progression be x, then the first term in the sequence is (75 – x), and the third term is (150 – x). The denominator of a geometric progression is equal to the ratio of the next member of the sequence to the previous member, i.e. в2 / в1 or в3 / в2. In our case, the denominator is x / (75 – x) or (150 – x) / x. Let’s make an equation and solve it.
x / (75 – x) = (150 – x) / x – apply the main property of proportion: the product of the extreme terms of the proportion is equal to the product of the middle terms of the proportion;
x * x = (75 – x) (150 – x);
x ^ 2 = 11250 – 150x – 75x + x ^ 2;
x ^ 2 + 150x + 75x – x ^ 2 = 11250;
225x = 11250;
x = 11250: 225;
x = 50 – 2nd term;
75 – 50 = 25 – 1st term;
150 – 50 = 100 – 3rd term.
Answer. 25; fifty; one hundred.