Tag: arithmetic mean of ap

Questions Related to arithmetic mean of ap

If $n^{th}$ term of AP is $4n+1$, then AM of $11^{th}$ to $ 20^{ th}$ terms is 

maths average arithmetic mean of ap introduction to averages means

  1. $61.5$

  2. $63$

  3. $63.5$

  4. $62$

Show answer
Correct Option: B
Explanation:

Given: $t _{n}=4n+1$

$A.M.=\cfrac{t _{11}+t _{20}}{2}$
           $=\cfrac{4\times 11+1+4\times 20+1}{2}$
           $=63$

If  $n^{th}$ term of AP is $t _n=4n+1$. Find mean of first $10$ terms.   

maths average arithmetic mean of ap introduction to averages means

  1. $85$

  2. $95$

  3. $23$

  4. $7.5$

Show answer
Correct Option: C
Explanation:
Given:
$t _{n}=4n+1$
$\therefore A.M.=\dfrac{\sum _{n=1}^{10}4n+1}{n}$
               $=\dfrac{2n(n+1)+n}{n}$
               $=2n+3$
               $=2\times 10+3$
               $=23$

Find AM of multiple of $3$  from natural numbers $1$ to $100$.

maths average arithmetic mean of ap introduction to averages means

  1. $48$

  2. $51$

  3. $36$

  4. $57$

Show answer
Correct Option: B
Explanation:

First term $=3$

Last term $=99$
$\therefore A.M.=\dfrac{3+99}{2}=51$

The  arithmatic mean of $4,6,8$ is

maths average arithmetic mean of ap introduction to averages means

  1. $4$

  2. $6$

  3. $8$

  4. $4.5$

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  First adding numbers $4,\, 6$ and $8$ = $4+6+8=18$

$\Rightarrow$   We have number of terms 3
$\Rightarrow$   $Arithemetic\, mean=\dfrac{S}{N}=\dfrac{18}{3}=6$

Find AM of  $ 3$  digit even numbers between $1$  to $500$.

maths average arithmetic mean of ap introduction to averages means

  1. $200$

  2. $400$

  3. $300$

  4. $150$

Show answer
Correct Option: C
Explanation:

First term $=100$

Last term $=500$
$\therefore A.M.=\cfrac{100+500}{2}=300$

Find AM of divisors of $100$.

maths average arithmetic mean of ap introduction to averages means

  1. $24$

  2. $25.5$

  3. $24.11$

  4. $21.9$

Show answer
Correct Option: C
Explanation:

Divisors of 100 are:

$1, 2, 4, 5, 10, 20, 25, 50, 100$
$\therefore n=9$
$\therefore S=1+2+4+5+10+20+25+50+100=217$
$\therefore A.M.=\dfrac{S}{n}=\dfrac{217}{9}=24.11$

If the nth term of AP is $2n+5$. Then find the  AM of first $38$  terms.

maths average arithmetic mean of ap introduction to averages means

  1. $99$

  2. $98$

  3. $100$

  4. $44$

Show answer
Correct Option: D
Explanation:
Given:
$t _{n}=2n+5$
First term $=2\times 1+5=7$
Last term $=2\times 38+5=81$
$\therefore A.M.=\dfrac{7+81}{2}=44$

The AM of  multiple of $5$ from numbers $1$ to $500$ is

maths average arithmetic mean of ap introduction to averages means

  1. $250$

  2. $\dfrac{500}{2}$

  3. $\dfrac{505}{2}$

  4. $252.5$

Show answer
Correct Option: D
Explanation:

First term $=5$

Last term $=500$
$\therefore A.M.=\dfrac{5+500}{2}=252.5$

The  Sum of three numbers in AP is $75$, and product of extremities is $609$. The numbrs and AM of 1st two numbers is 

maths average arithmetic mean of ap introduction to averages means

  1. ${21,25,29}$, AM $= 23$

  2. ${13,17,21}$, AM $= 22$

  3. ${21,25,29}$, AM $= 25$

  4. ${21,22,29}$, AM $= 23$

Show answer
Correct Option: A
Explanation:

Let the numbers in A.P.  be (a-d), a, (a+d)

$\therefore (a-d)+a+(a+d)=75$
$\Rightarrow a=25$
Also, $(a-d)(a+d)=609$
$\Rightarrow a^{2}-d^{2}=609$
$\Rightarrow 25^{2}-d^{2}=609$
$\therefore d=\pm4$
The numbers are {21,25,29} or {29,25,21}
According to option, we take {21,25,29}
A.M. of 1st two numbers $=\dfrac{21+25}{2}=23$

If the Arithmetic mean of $8, 6, 4, x, 3, 6, 0$ is $4$; then the value of $x =$

maths average arithmetic mean of ap introduction to averages means

  1. $7$

  2. $6$

  3. $1$

  4. $4$

Show answer
Correct Option: C
Explanation:

Arithmetic mean $= \cfrac{\text{sum of all observations}}{\text{no. of observations}}$

$\Rightarrow 4=\cfrac { 8+6+4+x+3+6+0 }{ 7 } \ \Rightarrow 28=27+x\ \Rightarrow x=1$