Tag: means

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Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. $2n^{3}+6n^{2}+7n-2$
  2. $n^{3}+8n^{2}+7n-2$
  3. $2n^{3}+5n^{2}+6n-2$
  4. $2n^{3}+8n^{2}+7n-2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The arithmetic mean of a sequence is the sum of terms divided by the number of terms. For the given series, calculating the sum and dividing by n yields the expression in option D.

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. 10

  2. 20

  3. 30

  4. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The sum of squares of the first 7 natural numbers is 1^2 + 2^2 + 3^2 + 4^2 + 5^2 + 6^2 + 7^2 = 1 + 4 + 9 + 16 + 25 + 36 + 49 = 140. The mean is 140 / 7 = 20.

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. $a$
  2. $\cfrac { a+4 }{ 3 } $
  3. $\cfrac { a-4 }{ 3 } $
  4. $\cfrac { a }{ 2 } $
Reveal answer Fill a bubble to check yourself
B Correct answer
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

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. -1

  2. 1

  3. 2

  4. -2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. -1

  2. 1

  3. 2

  4. -2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

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

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

Multiple choice maths average arithmetic mean of ap introduction to averages means

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

  1. $\displaystyle a + \frac{nd}{2}$
  2. $\displaystyle a + \frac{(n - 1)d}{2}$
  3. $a + (n - 1) d$
  4. $a + nd$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

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