Find the sum of a geometric series with the following values: a1=10; r=0.5; n=4
I got: 17.3205
sum(n) = a(1 - r^n)/(1 - r)
= 10(1 - .5^4)/(.5)
= 18.75
how did you get 17.3205 ?
To find the sum of a geometric series, you can use the formula:
Sn = a1 * (1 - r^n) / (1 - r)
where Sn is the sum of the series, a1 is the first term, r is the common ratio, and n is the number of terms.
In this case, given a1 = 10, r = 0.5, and n = 4, we can substitute these values into the formula:
Sn = 10 * (1 - 0.5^4) / (1 - 0.5)
Now let's calculate it step by step:
First, let's calculate 0.5^4 = 0.0625.
Sn = 10 * (1 - 0.0625) / (1 - 0.5)
Next, subtract 0.0625 from 1:
Sn = 10 * (0.9375) / (1 - 0.5)
After that, subtract 0.5 from 1:
Sn = 10 * (0.9375) / (0.5)
Now, multiply 10 by 0.9375:
Sn = 9.375 / 0.5
Finally, divide 9.375 by 0.5:
Sn = 18.75
Therefore, the sum of the geometric series with a1 = 10, r = 0.5, and n = 4 is 18.75.