What is the first term of a geometric series with a summation of 800, 4 terms and a common ratio of 3?
easy way:
1,3,9,27 adds to 40
800/40 = 20
so, 20,60,180,540
or,
a(1+r+r^2+r^3) = a(r^4-1)/(r-1) = a*80/2 = 40a
so, a = 800/40 = 20
Thank you, I think I understand how to work it out now! That helped me out so much!
To find the first term of a geometric series, you need to have the sum of the series, the number of terms, and the common ratio. In this case, we have the summation of 800, 4 terms, and a common ratio of 3.
The formula to find the sum of a geometric series is given by:
S = a * (r^n - 1) / (r - 1),
where:
S is the sum of the series,
a is the first term,
r is the common ratio, and
n is the number of terms.
We can rearrange this formula to solve for the first term (a):
a = S * (r - 1) / (r^n - 1).
Now we can substitute the given values into the formula:
a = 800 * (3 - 1) / (3^4 - 1).
Calculating further:
a = 800 * 2 / (81 - 1).
a = 1600 / 80.
a = 20.
Therefore, the first term of the geometric series is 20.