Calculating the Sum of the First Eight Terms in a Geometric Series

To find the sum of the first eight terms of a geometric series, we need to first identify the common ratio (r) and the first term (a)

To find the sum of the first eight terms of a geometric series, we need to first identify the common ratio (r) and the first term (a).

From the given series, we can see that each term is obtained by multiplying the previous term by 2. This means the common ratio is 2.

The first term (a) in this series is 3.

Now, we can use the formula for the sum of a geometric series:

S = a * (1 – r^n) / (1 – r)

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

Plugging in the values for this particular series:

n = 8 (since we want to find the sum of the first eight terms)
a = 3 (the first term)
r = 2 (the common ratio)

S = 3 * (1 – 2^8) / (1 – 2)

Now let’s calculate the sum:

S = 3 * (1 – 256) / (1 – 2)
S = 3 * (-255) / (-1)
S = 765

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

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