The sum of the first and second terms is exponentially -10, and the sum of the second and third terms is -5

The sum of the first and second terms is exponentially -10, and the sum of the second and third terms is -5. Find the first three numbers in a sequence?

The n-th term of the geometric progression is determined from the formula:
b_n = b1 * q ^ (n – 1),
where b1 is the first term of the progression, and q is the denominator of the geometric progression;
From the problem statement
b1 + b2 = -10
and
b2 + b3 = -5;
b2 = b1 * q and b3 = b1 * q ^ 2;
Substituting into the equations:
b1 + b1 * q = -10;
b1 * q + b1 * q ^ 2 = -5;
From the second equation we get:
q * (b1 + b1 * q) = -5;
-10 * q = -5;
q = 1/2;
Find b1:
b1 + b1 * 1/2 = -10;
3 * b1 / 2 = -10;
b1 = -20/3;
Let’s find two more members of this progression:
b2 = 1/2 * (-20/3) = -10/3;
b3 = 1/4 * (-20/3) = -5/3.