Average of 5 consecutive integers starting with m is n . average of 6 consecutive integers starting

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4.Average

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The average of $5$ consecutive integers starting with $m$ is $n$. What is the average of $6$ consecutive integers starting with $( m +2) ?$

A

$\frac{2 n+5}{2}$

B

$(n+2)$

C

$(n+3)$

D

$\frac{2 n+9}{2}$

Solution

Let the $5$ consecutive integers be $m , m +1, m +2, m +3, m +4$

$m+m+1+m+2+m+3+m+4=5 n$

$5 m+10=5 n \Rightarrow n=m+2$

Now, the average of $6$ consective number starting with $( m +2)$

$=\frac{[m +2+ m +3+ m +4+m+5+m+6+m+7]}{6}=\frac{6 m+27}{6}$

$=\frac{2 m+9}{2}=\frac{2(n-2)+9}{2}=\frac{2 n+5}{2}$

Standard 13

Quantitative Aptitude

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