Find the sum of the third through seventh terms of the geometric series whose first term is 5 and the common ratio is 3.(1 point)
To find the sum of the third through seventh terms of a geometric series, we can use the formula for the sum of the first n terms of a geometric series:
S_n = a * (1 - r^n) / (1 - r)
where:
S_n = sum of the first n terms
a = first term
r = common ratio
n = number of terms
In this case, a = 5, r = 3, and we want to find the sum of the third through seventh terms (n=7).
Plugging the values into the formula:
S_7 = 5 * (1 - 3^7) / (1 - 3)
S_7 = 5 * (1 - 2187) / -2
S_7 = 5 * (-2186) / -2
S_7 = -10930 / -2
S_7 = 5465
Therefore, the sum of the third through seventh terms of the geometric series is 5465.