Difference between sums of two series of n consecutive natural numbers is n2. Then which of the following is false?a)Difference between the largest and the smallest number is 2n.b)Among the largest terms of the two series, one is double of the other.c)Difference between the averages of two series is n + 1.d)All of theseCorrect answer is option 'D'. Can you explain this answer?

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Difference between sums of two series of n consecutive natural numbers is n². Then which of the following is false?

a)
Difference between the largest and the smallest number is 2n.
b)
Among the largest terms of the two series, one is double of the other.
c)
Difference between the averages of two series is n + 1.
d)
All of these

Correct answer is option 'D'. Can you explain this answer?

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Difference between sums of two series of n consecutive natural numbers...

Let (p + 1), (p + 2),..., (p + n) and (g + 1), (g + 2), ...(q + n) are the two series.
(p + 1) + (P + 2) + ... + (p + n) = np + n(n -1 )/2
(q + 1) + (q + 2) + ... + (q + n) = nq +n (n -1 )/2
Without loss o f generality, let p > q
np + n(n —1)/2 - nq + n(n -1)/2 = n (p - q) = n²
(p - q) = n
1. The largest number = (p + n) and the smallest number is (q + 1). (p + n) - (q + 1) = (p - q) + (n - 1) =n + (n - 1) = 2n - 1
2. (p + n) and (g + n) are the two largest terms of the two series. (p + n) - 2(q + n)

3. Average o f (p + 1), (p + 2)..... (p + n) = p + (n - 1 )/2
Average of (q + 1), (q + 2), ...(q + n) = q + (n -1 )/2
p + (n -1)/2 - q + (n -1)/2 = n
Thus, all the options are false.
Hence, option 4.

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Difference between sums of two series of n consecutive natural numbers is n2. Then which of the following is false?a)Difference between the largest and the smallest number is 2n.b)Among the largest terms of the two series, one is double of the other.c)Difference between the averages of two series is n + 1.d)All of theseCorrect answer is option 'D'. Can you explain this answer?

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Difference between sums of two series of n consecutive natural numbers is n2. Then which of the following is false?a)Difference between the largest and the smallest number is 2n.b)Among the largest terms of the two series, one is double of the other.c)Difference between the averages of two series is n + 1.d)All of theseCorrect answer is option 'D'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Difference between sums of two series of n consecutive natural numbers is n2. Then which of the following is false?a)Difference between the largest and the smallest number is 2n.b)Among the largest terms of the two series, one is double of the other.c)Difference between the averages of two series is n + 1.d)All of theseCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Difference between sums of two series of n consecutive natural numbers is n2. Then which of the following is false?a)Difference between the largest and the smallest number is 2n.b)Among the largest terms of the two series, one is double of the other.c)Difference between the averages of two series is n + 1.d)All of theseCorrect answer is option 'D'. Can you explain this answer?.

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