Find the first term of a geometric progression (Xn) if x5 = -64; q = -2.

Given: (Xn) – geometric progression;

x5 = -64, q = -2;

Find: x1 -?

Formula of the nth term of a geometric progression:

xn = x1 * q ^ (n-1), where:

x1 is the first term of the progression, q is the denominator of the progression.

This means that the fifthsq term of a given progression can be written in the following form:

x5 = x1 * q ^ (5-1) = x1 * q ^ 4.

Substituting all the quantities known by the condition into the resulting expression, we get:

x1 * (-2) ^ 4 = -64;

x1 * 16 = -64;

x1 = -64: 16;

x1 = -4.

Answer: x1 = -4.