Calculate S_12 for the geometric series 256-128+64-32+… using the finite geometric sum formula. Round to the nearest three decimal places

Answer 1

The first term of the series is 256 and the common ratio is -0.5.

Using the formula for the sum of a finite geometric series, the sum S_12 is given by:

S_12 = a * (1 - r^n) / (1 - r)

where a is the first term, r is the common ratio, and n is the number of terms.

Let's plug in the values:

S_12 = 256 * (1 - (-0.5)^12) / (1 - (-0.5))

Simplifying:

S_12 = 256 * (1 - 0.000244141) / (1 + 0.5)

S_12 = 256 * 0.999755859 / 1.5

S_12 = 383.474609 / 1.5

S_12 ≈ 255.65

Rounded to three decimal places, the sum S_12 is approximately 255.65.