What is the sum of the first 12 terms of the geometric series below 1/2+2+8+32+
In order to find the sum of the first 12 terms of the geometric series, we need to find the common ratio, r.
The second term (2) divided by the first term (1/2) gives us:
2 ÷ (1/2) = 2 × 2 = 4
The third term (8) divided by the second term (2) gives us:
8 ÷ 2 = 4
The common ratio, r, is equal to 4.
Now, we can use the formula for the sum of a finite geometric series to find the sum of the first 12 terms:
Sum = (first term) × (1 - r^n) / (1 - r)
Plugging in the values:
Sum = (1/2) × (1 - 4^12) / (1 - 4)
Sum = (1/2) × (1 - 16,777,216) / -3
Sum = (1/2) × (-16,777,215) / -3
Sum ≈ 27,960,358.33
Therefore, the sum of the first 12 terms of the geometric series is approximately 27,960,358.33.