Calculating the Sum of the First Eight Terms in a Geometric Series: Formula and Step-by-Step Guide

Find sum of the first eight terms of the geometric series; 3+6+12+…

To find the sum of the first eight terms of the geometric series, we need to first determine the common ratio (r) of the series

To find the sum of the first eight terms of the geometric series, we need to first determine the common ratio (r) of the series. We can do this by dividing any term in the series by the preceding term.

Let’s take the second term (6) and divide it by the first term (3):

r = 6 / 3
r = 2

Now that we know the common ratio is 2, we can use the formula to find the sum of the first n terms of a geometric series:

Sn = a * (1 – r^n) / (1 – r),

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

In our case:
a = 3 (the first term),
r = 2 (the common ratio),
n = 8 (the number of terms).

Let’s substitute these values into the formula and solve for Sn:

Sn = 3 * (1 – 2^8) / (1 – 2)
Sn = 3 * (1 – 256) / (-1)
Sn = 3 * (-255) / (-1)
Sn = -3 * 255
Sn = -765

Therefore, the sum of the first eight terms of the geometric series 3+6+12+… is -765.

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