In the sequence, r, s, t, if each term after the first is x more than the previous term, what is the average of r, s, and t in terms of r and x?
A) r + x
B) r + x/3
C) r + 2x/3
D) r+x/3
E) 3(r+x)
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Let r=2 and x=3.datonman wrote:In the sequence, r, s, t, if each term after the first is x more than the previous term, what is the average of r, s, and t in terms of r and x?
A) r + x
B) r + x/3
C) r + 2x/3
D) r+x/3
E) 3(r+x)
Since each term is x=3 more than the previous term, we get:
r, s, t = 2, 5, 8.
Average of r, s and t = (2+5+8)/3 = 5. This is our target.
Now plug r=2 and x=3 into the answers to see which yields our target of 5.
Only A works:
r+x = 2+3 = 5.
The correct answer is A.
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Another approach:datonman wrote:In the sequence, r, s, t, if each term after the first is x more than the previous term, what is the average of r, s, and t in terms of r and x?
A) r + x
B) r + x/3
C) r + 2x/3
D) r+x/3
E) 3(r+x)
There's a nice rule that says, "In a set where the numbers are equally spaced, the mean will equal the median."
Since each term is x greater than the term before it, these values are equally spaced.
So, the mean (average) = the median
Here, the median is s, so the average must be s
HOWEVER, the question wants the answer in terms of r and x.
We know that s is x greater than r
So, s = r + x
So, the mean = median = s = r + x
Answer: A
Cheers,
Brent
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Mathsbuddy
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The 3 terms are: r, r+x, r + 2x
The total is 3r + 3x
So the mean average is (3r + 3x)/3 = r + x
Answer = A
The total is 3r + 3x
So the mean average is (3r + 3x)/3 = r + x
Answer = A
