Given a geometric progression -24; -12; -6 find the sum of its first five members.

| September 15, 2021 | education

Let’s calculate the value of the denominator q. To do this, we will use the formula for calculating the nth term of the geometric progression: bn = b1 * qn – 1, therefore: qn – 1 = bn / b1.

In this case: bn = b2 = -12; b1 = -24; n = 2.

Let’s substitute the values into the formula:

q2 – 1 = -12 / (-24).

q = 1/2.

We apply the formula for the sum of the first n terms of a geometric progression: Sn = (b1 * (qn – 1)) / (q – 1).

Substitute the values b1 = -24 and q = 1/2 into the formula: S5 = (-24 * ((1/2) ^ 5 – 1)) / (1/2 – 1) = (-24 * (1 ^ 5 / 2 ^ 5 – 1)) / (1/2 – 2/2) = (-24 * (1/32 – 1)) / (-1/2) = (-24 * (-31/32)) / (-1/2) = ((24 * 31) / 32) / (-1/2) = 744/32 / (-1/2) = 23.25 / (-0.5) = -46, 5.

Answer: the sum of the first five members of the geometric progression S5 = -46.5.



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