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

It looks like you have a geometric progression with:

• First term b1 = -24
• Common ratio q = -1.5 (i.e., -3/2)

Then:

• General term: bn = b1 * q^(n-1) = -24 * (-1.5)^(n-1) = -24 * (-3/2)^(n-1)

  • Alternatively: bn = 24 * (-1)^n * (3/2)^(n-1)

• First terms: b1 = -24, b2 = 36, b3 = -54, b4 = 81, b5 = -121.5, ...

• Sum of first n terms: Sn = b1 * (1 - q^n) / (1 - q) = (-24) * (1 - (-1.5)^n) / (1 - (-1.5)) = (-24) * (1 - (-1.5)^n) / (2.5) = (-48/5) * (1 - (-1.5)^n) = (48/5) * [(-1.5)^n - 1]

• Note: since |q| > 1, the series does not converge as n → ∞.

If you want, tell me the exact thing you need (bn for a specific n, Sn for a given n, or something else) and I’ll compute it.