Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 717

If mean of first \(n\) odd natural Integer is \(n\) then \(n\) is (a) 2 (b) 3 (c) 1 (d) any natural integer

Short Answer

Expert verified
The correct answer is \( (d) \) any natural integer.

Step by step solution

01

Write down the first n odd natural integers

To find the first n odd natural integers, we can represent them as: 1, 3, 5, ... , (2n - 1)
02

Calculate the sum of the first n odd natural integers

The sum of an arithmetic series is given by: Sum = (number of terms / 2) × (first term + last term) In our case, the number of terms = n, first term = 1, last term = 2n - 1. So, Sum = (n / 2) × (1 + (2n - 1)) Simplifying the equation, Sum = (n / 2) × (2n) Sum = n^2
03

Calculate the mean of the first n odd natural integers

The mean is given by the sum of the first n odd natural integers divided by the number of integers, which is n. Mean = (Sum of first n odd natural integers) / n Mean = (n^2) / n Mean = n
04

Compare the obtained mean with the given possible values of n

We have obtained the mean as n. Now we will check if the mean is equal to any of the given options. Option (a): 2 Option (b): 3 Option (c): 1 Option (d): any natural integer We know that the mean is equal to the value of n itself. This means that any natural integer could be a possible value for n.
05

Choose the correct option

Since the mean of the first n odd natural integers is equal to any natural integer value of n, the correct answer is: Option (d): any natural integer

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

If mean of observations \(\mathrm{x}_{1}, \mathrm{x}_{2}, \mathrm{x}_{3}\) and \(\mathrm{x}_{4}\) is \(\underline{\mathrm{x}}\) and difference of first three observations with respect to \(\underline{x}\) is respectively \(-1,-3,-5\) then difference of fourth observation with respect to \(\underline{x}\) is (a) 8 (b) 9 (c) 10 (d) 11

A student obtain \(75 \%, 80 \%\) and \(85 \%\) in three subjects. If the marks of another subject are added then his average cannot be less then (a) \(60 \%\) (b) \(65 \%\) (c) \(80 \%\) (d) \(90 \%\)

Two numbers a and \(\mathrm{b}\) are chosen from a set of first 30 natural numbers. The probability that \(a^{2}-b^{2}\) is divisible by 3 is (a) \((9 / 87)\) (b) \((12 / 87)\) (c) \((15 / 87)\) (d) \((47 / 87)\)

For three events \(A, B, C\) \(P(\) exactly one of \(A\) or \(B\) occur \()=P\) \(P(\) exactly one of \(B\) or \(C\) occur \()=P\) \(P(\) exactly one of \(C\) or \(A\) occur \()=P\) And \(P(\) all three occur \()=P^{2} .\) Where \(0

3 dice are tossed. Find the probability that sum of digits is 14 (a) \(\left(21 / 6^{3}\right)\) (b) \(\left(15 / 6^{3}\right)\) (c) \(\left(27 / 6^{3}\right)\) (d) \(\left(16 / 6^{3}\right)\)
See all solutions

Recommended explanations on English Textbooks

Blog

Read Explanation

5 Paragraph Essay

Read Explanation

Lexis and Semantics

Read Explanation

Textual Analysis

Read Explanation

Rhetorical Analysis Essay

Read Explanation

Phonology

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free