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The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2?
- a)2 + s + a
- b)22 + a
- c)2s
- d)2a + 2
- e)4 + a
Correct answer is option 'E'. Can you explain this answer?
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Verified Answer
The arithmetic mean of the 5 consecutive integers starting with 's...
The sequence starts with 's' and its mean is 'a'
The mean of 5 consecutive numbers is the 3rd term - the middle term.
Hence, 'a'
the mean is the middle (3rd) term.The terms of the sequence are s, s + 1, s + 2, s + 3, and s + 4
The middle term is s + 2
Therefore, a = s + 2
The second series starts from s + 2
The terms will therefore, be s + 2, s + 3, s + 4, s + 5, s + 6, s + 7, s + 8, s + 9, and s + 10
The middle term of the second series is the 5th term = s + 6
If a = s + 2, then s + 6 will be a + 4
The average of the second sequence is a + 4
The mean of 5 consecutive numbers is the 3rd term - the middle term.
Hence, 'a'
the mean is the middle (3rd) term.The terms of the sequence are s, s + 1, s + 2, s + 3, and s + 4
The middle term is s + 2
Therefore, a = s + 2
The second series starts from s + 2
The terms will therefore, be s + 2, s + 3, s + 4, s + 5, s + 6, s + 7, s + 8, s + 9, and s + 10
The middle term of the second series is the 5th term = s + 6
If a = s + 2, then s + 6 will be a + 4
The average of the second sequence is a + 4
Most Upvoted Answer
The arithmetic mean of the 5 consecutive integers starting with 's...
The Arithmetic Mean of 5 Consecutive Integers Starting with s
To find the arithmetic mean of a set of numbers, we sum all the numbers in the set and divide by the total count of numbers.
Let's call the first integer in the set s. The next four consecutive integers will be s+1, s+2, s+3, and s+4.
The sum of the five integers can be calculated as:
s + (s+1) + (s+2) + (s+3) + (s+4) = 5s + 10
The arithmetic mean of these five integers is:
(5s + 10) / 5 = s + 2
The Arithmetic Mean of 9 Consecutive Integers Starting with s+2
Now, we want to find the arithmetic mean of nine consecutive integers starting from s+2.
The nine integers will be (s+2), (s+2)+1, (s+2)+2, (s+2)+3, (s+2)+4, (s+2)+5, (s+2)+6, (s+2)+7, and (s+2)+8.
The sum of these nine integers can be calculated as:
(s+2) + [(s+2)+1] + [(s+2)+2] + [(s+2)+3] + [(s+2)+4] + [(s+2)+5] + [(s+2)+6] + [(s+2)+7] + [(s+2)+8]
= 9s + 54
The arithmetic mean of these nine integers is:
(9s + 54) / 9 = s + 6
Comparison of Mean Values
We are given that the arithmetic mean of the five consecutive integers starting with s is a. Therefore, we have:
s + 2 = a
To find the arithmetic mean of the nine consecutive integers starting with s+2, we substitute the value of s+2 into the expression for the mean:
(s+2) + 6 = (a + 6)
Since the arithmetic mean of the nine consecutive integers starting with s+2 is (a + 6), we can conclude that the correct answer is option E: 4 + a.
To find the arithmetic mean of a set of numbers, we sum all the numbers in the set and divide by the total count of numbers.
Let's call the first integer in the set s. The next four consecutive integers will be s+1, s+2, s+3, and s+4.
The sum of the five integers can be calculated as:
s + (s+1) + (s+2) + (s+3) + (s+4) = 5s + 10
The arithmetic mean of these five integers is:
(5s + 10) / 5 = s + 2
The Arithmetic Mean of 9 Consecutive Integers Starting with s+2
Now, we want to find the arithmetic mean of nine consecutive integers starting from s+2.
The nine integers will be (s+2), (s+2)+1, (s+2)+2, (s+2)+3, (s+2)+4, (s+2)+5, (s+2)+6, (s+2)+7, and (s+2)+8.
The sum of these nine integers can be calculated as:
(s+2) + [(s+2)+1] + [(s+2)+2] + [(s+2)+3] + [(s+2)+4] + [(s+2)+5] + [(s+2)+6] + [(s+2)+7] + [(s+2)+8]
= 9s + 54
The arithmetic mean of these nine integers is:
(9s + 54) / 9 = s + 6
Comparison of Mean Values
We are given that the arithmetic mean of the five consecutive integers starting with s is a. Therefore, we have:
s + 2 = a
To find the arithmetic mean of the nine consecutive integers starting with s+2, we substitute the value of s+2 into the expression for the mean:
(s+2) + 6 = (a + 6)
Since the arithmetic mean of the nine consecutive integers starting with s+2 is (a + 6), we can conclude that the correct answer is option E: 4 + a.
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The arithmetic mean of the 5 consecutive integers starting with 's' is 'a'. What is the arithmetic mean of 9 consecutive integers that start with s + 2?a)2 + s + ab)22 + ac)2sd)2a + 2e)4 + aCorrect answer is option 'E'. Can you explain this answer?
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