What is the sum of the first seven terms of a series whose first term is 2 and has a common ratio of 4?(1 point)
250
1000
10,922
14,630
14,630
To find the sum of the first seven terms, we use the formula for the sum of a geometric series:
S = a * (1 - r^n) / (1 - r)
Where:
S is the sum of the first n terms
a is the first term (2)
r is the common ratio (4)
n is the number of terms (7)
Plugging in the values, we get:
S = 2 * (1 - 4^7) / (1 - 4)
S = 2 * (1 - 16384) / -3
S = 2 * (-16383) / -3
S = -32766 / -3
S = 10,922
Therefore, the sum of the first seven terms of the series is 10,922.