Question

We can set up an equation to help us solve this problem. Let's define a variable. 

Let n be the smallest  number. We have $n + n+1 + n+2 ....... n+6 = 7n + 21$

Now, this sequence adds up to 28/5 times the largest number, n + 6, so we can write the equation

$7n+21=28/5(n+6)$

From here, we just solve for n. We have

$7n+21=\frac{28}{5}n + 168/5\\ 7/5n=63/5$

Now, multiplying both sides by the reciprocol of 7/5, we get

$n=\frac{63}{5} \cdot \frac{5}{7}=9$

So 9 is our final answer!

Thanks! :)