The average of 5 consecutive integers startin | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Let the $5$ consecutive integers starting with $m$ be $m, m + 1, m + 2, m + 3, m + 4$.The average is given by: $\frac{m + (m + 1) + (m + 2) + (m +

Vedclass · Accepted Answer

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

Vedclass · Answer

(A) Let the $5$ consecutive integers starting with $m$ be $m, m + 1, m + 2, m + 3, m + 4$.The average is given by: $\frac{m + (m + 1) + (m + 2) + (m + 3) + (m + 4)}{5} = n$.Simplifying the numerator: $\frac{5m + 10}{5} = n$,which gives $m + 2 = n$.Now,we need the average of $6$ consecutive integers starting with $(m + 2)$. These integers are $(m + 2), (m + 3), (m + 4), (m + 5), (m + 6), (m + 7)$.The average is: $\frac{(m + 2) + (m + 3) + (m + 4) + (m + 5) + (m + 6) + (m + 7)}{6}$.Summing the terms: $\frac{6m + 27}{6} = m + \frac{27}{6} = m + 4.5$.Since $m = n - 2$,substitute this into the expression: $(n - 2) + 4.5 = n + 2.5$.Converting to fraction form: $n + \frac{5}{2} = \frac{2n + 5}{2}$.

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

Similar Questions

The average of $30$ numbers is $15$. The average of the first $18$ numbers is $10$ and that of the next $11$ numbers is $20$. The last number is:

The average marks obtained by a class of $60$ students is $65$. The average marks of half of the students is found to be $85$. The average marks of the remaining students is:

If the difference between the average of $x, y$ and $y, z$ is $12,$ then the difference between $x$ and $z$ is

The average weight of $36$ students is $50 \,kg$. It was found later that the weight of one of the students was misread as $73 \,kg$,whereas his actual weight was $37 \,kg$. Find the correct average (in $kg$).

Of the three numbers,the second is twice the first and is also thrice the third. If the average of the three numbers is $44,$ the largest number is

Vedclass Test Series

Exam Paper Generator

Online Exam Module