What is the first term of a geometric series with a summation of 800, 4 terms and a common ratio of 3?
To find the first term of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r)
where S is the summation of the series, a is the first term, r is the common ratio, and n is the number of terms.
In this case, we are given the following information:
S = 800 (summation)
n = 4 (number of terms)
r = 3 (common ratio)
We can substitute these values into the formula and solve for a:
800 = a * (1 - 3^4) / (1 - 3)
Simplifying the equation:
800 = a * (1 - 81) / -2
We can further simplify the equation:
800 = a * (-80) / -2
Multiplying both sides by -2:
-1600 = a * (-80)
Dividing both sides by -80:
a = -1600 / -80
Calculating:
a = 20
Therefore, the first term of the geometric series is 20.