The average of five consecutive positive inte | vedclass

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(C) Let the five consecutive integers be $x, x+1, x+2, x+3, x+4$.The average of these five integers is given by $\frac{x + (x+1) + (x+2) + (x+3) + (x+

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increase by $1$

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(C) Let the five consecutive integers be $x, x+1, x+2, x+3, x+4$.The average of these five integers is given by $\frac{x + (x+1) + (x+2) + (x+3) + (x+4)}{5} = \frac{5x + 10}{5} = x + 2$.Given that the average is $n$,so $n = x + 2$.Now,if the next two integers ($x+5$ and $x+6$) are included,the total number of integers becomes $7$.The sum of these seven integers is $(5x + 10) + (x+5) + (x+6) = 7x + 21$.The new average is $\frac{7x + 21}{7} = x + 3$.Since the original average was $n = x + 2$,the new average $x + 3$ can be written as $(x + 2) + 1 = n + 1$.Therefore,the average increases by $1$.

The average of five consecutive positive integers is $n$. If the next two integers are also included,the average of all these integers will

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