Geometric progression. Given a geometric progression (bn): 2048; -256; 32; … Find the sum of its first five members.

Knowing the first two terms of the geometric progression, we determine its denominator.

q = -256/2048 = -1/8 = -0.125.

Let’s define the fifth term of the progression.

b5 = b1 * q4 = 2048 / (-1/8) 4 = 2048/4096 = 0.5.

Let’s determine the sum of the first five members of the progression.

Sn = (bn * q – b1) / (q – 1).

Sn = (0.5 * (-0.125) – 2048) / (-1/8 – 1) = – 2048.0625 / (-9/8) = 2048.0625 * 8/9 = 1820.5.

Answer: The sum of the five members of the progression is 1820.5.