what is the sum of the first seven terms of a series whole first term is 2 and has a common ratio of 4

1 answer

To find the sum of the first seven terms of a geometric series, we use the formula:

S = a * (r^n - 1) / (r - 1)

Where:
S = sum of the first n terms
a = first term
r = common ratio
n = number of terms

Given:
a = 2
r = 4
n = 7

Plugging in the values, we get:

S = 2 * (4^7 - 1) / (4 - 1)
S = 2 * (16384 - 1) / 3
S = 2 * 16383 / 3
S = 32766 / 3
S = 10922

Therefore, the sum of the first seven terms of the series is 10922.