b, = -24, q = -1,5;

I think you’re giving a geometric progression: b1 = -24 and common ratio q = -1.5 (note -1,5 means -1.5).

Then the standard formulas are:

• nth term: b_n = b1 · q^(n-1) = -24 · (-1.5)^(n-1)
• Sum of first n terms: S_n = b1 · (1 − q^n) / (1 − q) = -24 · (1 − (-1.5)^n) / (1 − (-1.5)) = -24 · (1 − (-1.5)^n) / 2.5 = -9.6 · (1 − (-1.5)^n)
• The infinite sum does not converge (|q| = 1.5 > 1).

Example:

• b2 = -24 · (-1.5) = 36
• b3 = -24 · (-1.5)^2 = -54
• S4 = -9.6 · (1 − (-1.5)^4) = -9.6 · (1 − 5.0625) = -9.6 · (-4.0625) = 39

If you meant something different (e.g., b is not the first term, or you want a specific n, or a sum to N), please share the exact problem statement and what you’re solving for.