The first term of geometric series is 124 .The sum to infinity is 64 find the common ratio
124/(1-r) = 64
124/(1-r)=64
We have the formula for the sum to infinity of a geometric series:
S = a / (1 - r), where a is the first term and r is the common ratio.
Given that the first term (a) is 124 and the sum to infinity (S) is 64, we can substitute these values into the formula and solve for the common ratio:
64 = 124 / (1 - r)
To isolate r, we can multiply both sides of the equation by (1 - r):
64(1 - r) = 124
Expanding and rearranging the terms:
64 - 64r = 124
Subtracting 64 from both sides:
-64r = 60
Dividing both sides by -64:
r = 60 / (-64)
Simplifying the fraction:
r = -15 / 16
Therefore, the common ratio of the geometric series is -15/16.
To find the common ratio of a geometric series, we need to use the formula for the sum of an infinite geometric series.
The formula for the sum of an infinite geometric series is:
S = a / (1 - r)
Where:
S = sum of the series
a = first term of the series
r = common ratio of the series
In this case, we are given that the first term (a) is 124 and the sum to infinity (S) is 64.
Let's substitute these values into the formula and solve for the common ratio (r):
64 = 124 / (1 - r)
To simplify, we can cross multiply:
64 * (1 - r) = 124
Expanding and rearranging the equation:
64 - 64r = 124
Again, rearranging the equation:
64r = 124 - 64
64r = 60
Dividing both sides by 64:
r = 60 / 64
Simplifying the fraction:
r = 15 / 16
Therefore, the common ratio of the geometric series is 15 / 16.