find the sum of the first 10 terms of geometric series with a[2]=(1)/(2) and r=2
would it be s[10]=1(1-2^10)/(1-2) answer 1023
the second term is ar , and r = 2
so 2a = 1/2
a = 1/4
sum(10) = a(r^10 - 1)/(r-1)
= (1/4)(2^10 - 1)/(2-1)
= (1/4)(1023) = 1023/4 or 255.75
To find the sum of the first 10 terms of a geometric series, we can use the formula:
S = a * (1 - r^n) / (1 - r),
where:
S is the sum of the series,
a is the first term of the series,
r is the common ratio of the series,
n is the number of terms in the series.
Given that a[2] = 1/2 and r = 2, we need to find the value of a, the first term of the series.
In a geometric series, each term is obtained by multiplying the previous term by the common ratio.
We are given a[2] = 1/2, which means the second term of the series, a[2], is equal to a * r. Substituting the values into the equation, we get:
1/2 = a * 2.
Simplifying the equation, we find:
a = 1/4.
Now we have the value of a and the common ratio r. We can plug these values into the formula to find the sum of the first 10 terms.
S = (1/4) * (1 - 2^10) / (1 - 2).
Simplifying further, we get:
S = (1/4) * (-1023) / (-1).
Simplifying the expression, the sum of the first 10 terms of the geometric series is:
S = 1023/4.
Therefore, the sum of the first 10 terms of the given geometric series is 1023/4.