The sum of an inifinte geometric series is 4.5 and the first term is 3. Determine the common ratio.
A. 1/3
B. 3/4
C. -1/2
D. -3/4
Is it B?
3/(1-r) = 9/2
2/3 = 1-r
r = 1/3
To determine the common ratio of an infinite geometric series, we can use the formula:
S = a / (1 - r),
where S is the sum of the series, a is the first term, and r is the common ratio.
Given that the sum (S) is 4.5 and the first term (a) is 3, we can substitute these values into the formula:
4.5 = 3 / (1 - r).
Now, we can solve for the common ratio (r):
4.5(1 - r) = 3
4.5 - 4.5r = 3
4.5r = 4.5 - 3
4.5r = 1.5
r = 1.5 / 4.5
r = 1/3
Therefore, the common ratio is 1/3. Thus, the correct answer is A.
To determine the common ratio of an infinite geometric series, we can use the formula for the sum of an infinite geometric series.
The sum of an infinite geometric series is given by the formula:
S = a / (1 - r)
Where:
S is the sum of the series,
a is the first term of the series,
and r is the common ratio.
In this case, we are given that the sum of the series is 4.5 and the first term is 3. So, we can substitute these values into the formula and solve for the common ratio:
4.5 = 3 / (1 - r)
To solve for r, we can start by isolating it on one side of the equation:
4.5(1 - r) = 3
Simplify the left side:
4.5 - 4.5r = 3
Now, let's isolate the term with r:
4.5r = 4.5 - 3
4.5r = 1.5
Divide both sides by 4.5:
r = 1.5 / 4.5
r = 1/3
Therefore, the common ratio of the infinite geometric series is 1/3. So, the correct answer is option A.