The geometric progression is specified by the condition bn = -78.5 * (- 2) ^ n. Find the sum of the first 4 members.

Let us find successively the first four terms of a given geometric progression, and then we find the sum of these terms.

Substituting the values n = 1, n = 2, n = 3 and n = 4 into the formula for the nth term bn = -78.5 * (-2) ^ n of this progression, we get:

b1 = -78.5 * (-2) ^ 1 = -78.5 * (1/2);

b2 = -78.5 * (-2) ^ 2 = -78.5 * (1/4);

b3 = -78.5 * (-2) ^ 3 = -78.5 * (1/8);

b4 = -78.5 * (-2) ^ 4 = -78.5 * (1/16).

We find the sum of the first four members of this geometric progression:

b1 + b2 + b3 + b4 = -78.5 * (1/2) – 78.5 * (1/4) – 78.5 * (1/8) – 78.5 * (1/16) = -78.5 * (1/2 + 1 / 4 + 1/8 + 1/16) = -78.5 * (8/16 + 4/16 + 2/16 + 1/16) = -78.5 * (15/16) = -70 25/32.

Answer: the sum of the first four members of this progression is -70 25/32.