Given a geometric progression, calculate the sum of the first 2 terms if b3 = 8 q = -2

1. In the calculations, we will use the formulas:

a) to find the value of any member of a geometric progression:

bn = b1 * g ^ (n – 1);

b) to determine the sum of any number of members:

Sn = (bn * g – b1): (g – 1).

2. By the condition of the problem, g = -2, b3 = 8.

Substitute the given values into the general formula and get:

b3 = b1 * (-2) ^ (3 – 1) = b1 * 2² = b1 * 4 = 8, whence b1 = 8: 4 = 2.

3. Find the sum of two terms

S2 = (b2 – b1): (-2 – 1) = (b1 * g – b1): (-3) = (-2 * 2 – 2): (-3) = 6/3 = 2.

Answer: S2 is 2.