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.
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)
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