Find the sum of first n terms and the sum of first 5 terms of the geometric series
what is the series
Sn = a(1-r^n)/(1-r)
so,
S5 = a(1-r^5)/(1-r)
I need the question answer
To find the sum of the first n terms of a geometric series, you can use the formula:
Sn = a * (1 - r^n) / (1 - r)
Where:
Sn is the sum of the first n terms of the series.
a is the first term of the series.
r is the common ratio.
Similarly, to find the sum of the first 5 terms, you can substitute n = 5 into the formula.
Let's say we have a geometric series with a first term of 2 and a common ratio of 3. We can calculate the sum of the first n terms and the sum of the first 5 terms using the formula.
For the sum of the first n terms:
Sn = 2 * (1 - 3^n) / (1 - 3)
For the sum of the first 5 terms:
S5 = 2 * (1 - 3^5) / (1 - 3)
Now, you can substitute the values of a and r into the formulas and calculate the sums.
Sn = 2 * (1 - 3^n) / (1 - 3)
S5 = 2 * (1 - 3^5) / (1 - 3)