Question

Consider a sequence of seven consecutive integers. The average of the first five integers is $n$. The average of all the seven integers is

• A. $n$
• B. $n+1$
• C. $k\times n$, where $k$ is a function of $n$
• D. $n+\frac{2}{7}$

Answer 1

The correct option is B $n+1$

Let the seven consecutive integers be $x-3,x-2,x-1,x,x+1,x+2,x+3$

Given that average of first five integers is $n$

Therefore, $n=\frac{(x-3)+(x-2)+(x-1)+x+(x+1)}{5}$

$⟹5x-5=5n$

$⟹x-1=n$

$⟹x=n+1$ ------(1)

Average of seven integers is $\frac{(x-3)+(x-2)+(x-1)+x+(x+1)+(x+2)+(x+3)}{7}$

$=\frac{7x}{7}=x=n+1$ (from (1))