The first term of geometric is 124.the sum of infinity is 64.find the common ratio
a = 124
a/(1-r) = 64
124/(1-r) = 64
124 = 64 - 64r
r = -60/64 = -15/16
To find the common ratio in a geometric sequence, we can use the formula:
Sum = a / (1 - r)
Given that the first term (a) is 124 and the sum of infinity is 64, we can substitute these values into the formula:
64 = 124 / (1 - r)
Next, we need to solve for the common ratio (r). We can do this by multiplying both sides of the equation by (1 - r):
64 * (1 - r) = 124
Now, let's expand and simplify the equation:
64 - 64r = 124
Let's isolate the term containing r:
-64r = 124 - 64
Simplifying further:
-64r = 60
To solve for r, divide both sides of the equation by -64:
r = 60 / -64
r ≈ -0.9375
Therefore, the common ratio (r) is approximately -0.9375.
To find the common ratio in a geometric series, we need to use the formula for the sum of an infinite geometric series:
Sum = a / (1 - r),
where "a" is the first term of the series and "r" is the common ratio.
In this case, we are given that the first term is 124 and the sum of the infinite series is 64. Plugging these values into the formula, we get:
64 = 124 / (1 - r).
To find the common ratio "r," we need to isolate it. Let's begin by multiplying both sides of the equation by (1 - r):
64 * (1 - r) = 124.
Expanding the left side of the equation:
64 - 64r = 124.
Next, let's isolate "-64r" by subtracting 64 from both sides:
-64r = 124 - 64,
-64r = 60.
Now, divide both sides of the equation by -64:
r = 60 / -64,
r ≈ -0.9375.
Therefore, the common ratio of the geometric series is approximately -0.9375.