Tag: arithmetic mean of ap

Questions Related to arithmetic mean of ap

The $A.M.$ of the observations $1.3.5,3.5,7,9,.,(2n-1)(2n+1) (2n+3)$ is $(\forall\ n\ \in\ N)$

maths average arithmetic mean of ap introduction to averages means

  1. $2n^{3}+6n^{2}+7n-2$

  2. $n^{3}+8n^{2}+7n-2$

  3. $2n^{3}+5n^{2}+6n-2$

  4. $2n^{3}+8n^{2}+7n-2$

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Correct Option: D

The mean of ${1^{2,}}{2^2},{3^2},{4^2},{5^2},{6^2},{7^2}$ is:

maths average arithmetic mean of ap introduction to averages means

  1. 10

  2. 20

  3. 30

  4. None of these

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Correct Option: B

The A.M. of a + 2, a, 2-a is

maths average arithmetic mean of ap introduction to averages means

  1. $a$

  2. $\cfrac { a+4 }{ 3 } $

  3. $\cfrac { a-4 }{ 3 } $

  4. $\cfrac { a }{ 2 } $

Show answer
Correct Option: B
Explanation:

Given values are : $a+2, a, 2-a$


Arithmetic Mean, $AM = \dfrac{a+2+a+2-a}{3}$

$AM = \dfrac{a+4}{3}$

Hence, option B is corret

Find the mean of $ 43,54,64,53,36$

maths average arithmetic mean of ap introduction to averages means

  1. $50$

  2. $ 40$

  3. $60$

  4. $ 30$

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Correct Option: A
Explanation:

Given data $43,54,64,53,36$


Sum of observations $43+54+64+53+36=250$


No . of observations $5$

Mean of data $=\dfrac{250}{5}=50$

The arithmetic mean of $1 + \sqrt { 2 }$ and $7 + 5 \sqrt { 2 }$ is $\sqrt { a } + \sqrt { b }$ . Then $a - b =$

maths average arithmetic mean of ap introduction to averages means

  1. -1

  2. 1

  3. 2

  4. -2

Show answer
Correct Option: D
Explanation:

The arithmetic mean of $1+\sqrt{2}$ and $7+5\sqrt{2}$ is $\dfrac{1+\sqrt{2}+7+5\sqrt{2}}{2}=\dfrac{8+6\sqrt{2}}{2}=4+3\sqrt{2}=\sqrt{16}+\sqrt{18}$

$\implies \sqrt{a}+\sqrt{b}=\sqrt{16}+\sqrt{18}$
$\implies a=16,b=18$
$a-b=16-18=-2$

The airthmatic mean of $1 + \sqrt { 2 }$ and $7 + 5 \sqrt { 2 }$ is $\sqrt { a } + \sqrt { b }$ . Then a $- b =$

maths average arithmetic mean of ap introduction to averages means

  1. -1

  2. 1

  3. 2

  4. -2

Show answer
Correct Option: D
Explanation:

The arithmetic mean of $1+\sqrt{2}$ and $7+5\sqrt{2}$ is $\dfrac{1+\sqrt{2}+7+5\sqrt{2}}{2}=\dfrac{8+6\sqrt{2}}{2}=4+3\sqrt{2}=\sqrt{16}+\sqrt{18}$

$\implies \sqrt{a}+\sqrt{b}=\sqrt{16}+\sqrt{18}$
$\implies a=16,b=18$
$a-b=16-18=-2$

Mean of the first $n$ terms of the A.P. $a, (a + d), (a + 2d), ........$ is

maths average arithmetic mean of ap introduction to averages means

  1. $\displaystyle a + \frac{nd}{2}$

  2. $\displaystyle a + \frac{(n - 1)d}{2}$

  3. $a + (n - 1) d$

  4. $a + nd$

Show answer
Correct Option: B
Explanation:

Required mean $= \displaystyle \frac{a + (a + d) + (a + 2d) + ....... + { a + (n - 1) d }}{n}$
$\displaystyle = \frac{\displaystyle \frac{n}{2} [a + a + (n - 1) d]}{n} = a + \frac{(n - 1)d}{2}$

If the arithmetic mean of $6, 8, 5, 7, x$ and $4$ is $7,$ then $x$ is

maths average arithmetic mean of ap introduction to averages means

  1. $12$

  2. $6$

  3. $8$

  4. $4$

Show answer
Correct Option: A
Explanation:

By definition,
$\displaystyle AM=\frac{6+8+5+7+x+4}{6}=7$
or $x=12.$

Find the Arithmetic mean between 24 and 36 

maths average arithmetic mean of ap introduction to averages means

  1. 26

  2. 28

  3. 30

  4. 32

Show answer
Correct Option: C
Explanation:

The arithmetic mean(AM) between 2 numbers is the simple average of the two numbers.

So, AM = $\qquad \dfrac { 24\quad +\quad 36 }{ 2 } \ =\quad 30$.

AM = 30.

The arithmetic mean of $12$ and $20$ is :

maths average arithmetic mean of ap introduction to averages means

  1. $12$

  2. $14$

  3. $16$

  4. $18$

Show answer
Correct Option: C
Explanation:

The AM of two numbers is their average.
So, the AM of $12$ and $20$ is $ \dfrac { 12+ 20 }{ 2 }= 16$.