Answer:
57330
Step-by-step explanation:
To get the sum, we can use the formula:
Sₙ = [a₁(1 - rⁿ)]/(1 - r)
where:
Sₙ = the sum of the first n terms
a₁ = the first term
n = the number of terms
r = the common ratio, r ≠ 1
In the problem, the given values are:
a₁ = 14
n = 12
r = 2
Substitute these values to the formula above.
Sₙ = [a₁(1 - rⁿ)]/(1 - r)
S₁₂ = [14(1 - 2¹²)]/(1 - 2)
S₁₂ = [14(1 - 4096)]/(-1)
S₁₂ = [(14)(-4095)/(-1)
S₁₂ = (-57330)/(-1)
S₁₂ = 57330
The sum of the first 12 terms of the geometric series is 57330.
