What is the sum of a geometric series with first term a1= 2, a common ratio r of 2 and the number of terms, n, equal to 4.
sequence is 2,4,8,16
sum = 30
just FYI the series is the sequence of partial sums of the sequence:
series = 2,6,14,30,...
To find the sum of a geometric series, you can use the formula:
S = a1 * (1 - r^n) / (1 - r)
where S is the sum, a1 is the first term, r is the common ratio, and n is the number of terms.
Given a1 = 2, r = 2, and n = 4, we can substitute these values into the formula:
S = 2 * (1 - 2^4) / (1 - 2)
Simplifying the equation:
S = 2 * (1 - 16) / (1 - 2)
S = 2 * (-15) / (-1)
S = 30 / 1
S = 30
Therefore, the sum of the geometric series is 30.
To find the sum of a geometric series with a given first term, common ratio, and number of terms, you can use the formula:
Sn = a1 * (1 - r^n) / (1 - r)
where Sn represents the sum of the geometric series, a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, a1 = 2, r = 2, and n = 4. Let's substitute these values into the formula:
S4 = 2 * (1 - 2^4) / (1 - 2)
Now we can simplify the equation:
S4 = 2 * (1 - 16) / (1 - 2)
= 2 * (-15) / (-1)
= 30
Therefore, the sum of the geometric series with first term a1 = 2, common ratio r = 2, and number of terms n = 4 is 30.